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Automated detection and quantification of petit mal seizures in the electroencephalogram

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Automated detection and quantification of petit mal seizures in the electroencephalogram
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Principe, Jose Carlos Santos Carvalho, 1950-
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viii, 364 leaves : ill. ; 28 cm.

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Amplitude ( jstor )
Digital filters ( jstor )
Electroencephalography ( jstor )
Microcomputers ( jstor )
Seizures ( jstor )
Signal to noise ratios ( jstor )
Signals ( jstor )
Sine function ( jstor )
Statistical discrepancies ( jstor )
Waveforms ( jstor )
Dissertations, Academic -- Electrical Engineering -- UF
Electrical Engineering thesis Ph. D
Electroencephalography ( lcsh )
Epilepsy ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 333-345.
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Jose Carlos Santos Carvalho Principe.

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University of Florida
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Copyright Jose Carlos Santos Carvalho Principe. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
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AUTOMATED DETECTION AND QUANTIFICATION
OF PETIT MAL SEIZURES IN THE ELECTROENCEPHALOGRAM









BY

JOSE CARLOS SANTOS CARVALHO PRINCIPE


A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY






UNIVERSITY OF FLORIDA


1979















ACKNOWLEDGEMENT S


The author would like to thank his supervisory

committee for their aid, guidance and criticism during the preparation of this dissertation. Especially the author would like to thank Dr. Jack Smith for his willingness to share facilities, personal contacts and responsibilities. It was an unconventional but effective learning experience, which went beyond the restricted field of EEG studies. The friendly relationship created during these years is deeply appreciat�d.

There are many others who contributed their knowledge, skills and time for this dissertation to become a reality. The author would like to thank Sonny, Yvonne, Shiv, Nate, Dan, Alan and Salim for their large, small, direct or indirect contributions. Special thanks go to Fred for his constant help*in the data collection phase.

The author also would like to thank the Department of Electrical Engineering of the University of Florida, Comissao Permanente INVOTAN (NATO--Portugal), and the Institute of International Education for the financial support received throughout his graduate studies.

The author sincerely thanks his family for their support and confidence, especially his wife for her constant









companionship in spite of the stress created by the long working hours devoted to the laboratory.


iii
















TABLE OF CONTENTS


Page

ACKNOWLEDGEMENTS . . ii

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . vi

CHAPTER

I LITERATURE SURVEY . . . . . 1

Spectral Analysis . 1
Time Domain Approach . . . . 18
Selection of the Method of Seizure
Detection . . . . . . . 25

II MICROCOMPUTER BASED DIGITAL FILTER DESIGN . . 30

Preliminary Considerations . . . . . 30
Design Criteria . . . . . . . . . . 35
Filter Transfer Function . . . 38
Lowpass to Bandpass Transformations . . . 41
Transformations to the Z Plane . . . . 43
Finite Length Effects of the
Implementation . . . 53
Practical Considerations . . . . . . 84

III A MODEL FOR PETIT MAL SEIZURES AND ITS
IMPLEMENTATION . . 94

Detection Problem . . . . . 94
A Petit Mal Seizure Model . . 98
Definition of the Implementation Scheme . . . 106
System Implementation . . . . . . . 136
Testing of the Program . . . . 157

IV SYSTEM EVALUATION AND PRESENTATION OF
RESULTS . 165

Description of Data Collection . . . . . 165
System Evaluation . . . . . . . . . . . . . . 170
Statistics of Seizure Data . . . 187
Analysis of the False Detections and
Proposed Improvement in the Detector . . . 224
Proposed System Utilization and Concluding
Remarks . . . . . 233











APPENDIX

I CHEBYSHEV FILTER DESIGN . . . . . . .

Chebyshev Polynomials . . . . . . . .
Automated Design . . . . . . . . . . .
Filter Design Program . . . . . . . .

II DIGITAL FILTER IMPLEMENTATION . . . .

Preliminary Considerations . . . . . .
Implementation of the Filter Algorithm

III FLOW CHARTS AND PROGRAM LISTINGS . . . REFERENCES . . . . . . . . . . . . . . . . . .

BIOGRAPHICAL SKETCH . . . . . . . . . . . . . .


Page


239 239 242 244 250 250
253 265 333

346


. . .


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Abstract of Dissertation Presented to the
Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy AUTOMATED DETECTION AND QUANTIFICATION
OF PETIT MAL SEIZURES IN THE ELECTROENCEPHALOGRAM By

Jose Carlos Santos Carvalho Principe August 1979

Chairman: Jack R. Smith
Major Department: Electrical Engineering

This dissertation deals with the automated analysis

and quantification of Petit Mal (PM) paroxysms in the human electroencephalogram (EEG). A petit-mal detector was built to help neurologists evaluate drug effectiveness in the treatment of PM epilepsy. The decision of basing the detection scheme in a microcomputer provided completely new directions for the design process because of the versatility and great computational capabilities of the machine.

The problem of nonrepeatability of characteristics in the analog filters was avoided by replacing them by digital filters. A microcomputer based digital filter design procedure was developed, taking into consideration the computation speed, the filter internal gain and the noise characteristics of different topologic structures. To yield sufficient output signal to noise ratio a 16 bit









microcomputer and a 12 bit A/D converter were utilized. With the procedure, a fourth order bandpass filtering function can be accomplished in less than 300 ps.

Time domain parameters were selected to arrive at a PM seizure model which would be applicable to the detection of classical PM and PM variant epilepsies. The parameters were translated into electronic quantities and implemented in a microcomputer.

For the first time in the automated analysis of EEG, a microcomputer based system was built for the processing of one channel of data, using a completely digital, real time, detection scheme. All the programs which comprise the detector were written in assembly language, and care was taken to reduce the interactions between program modules. The top-down program approach was utilized.

The system was tested and evaluated with data from

epileptics collected in the Veterans Administration Hospital, Neurology Service, from an ongoing drug study. A telemetry link was used to record the EEG, allowing the patient to move at will in a 3 x 5 meters room. Six patients who showed the largest number of seizures were selected for the evaluation. A total of 70 hours of data was analyzed.

The agreement in the detections with the human scorer, for seizures (Sz) greater than three seconds, was 86 percent. If the sorting of seizures in the groups 3 < Sz


vii









< 10 sec and Sz > 10 sec is taken into consideration, the agreement decreased to 77 percent.

Besides outputting the information about number of

seizures, their duration and time of occurrence, the detector also presents a detailed analysis of the detection parameters. These results, the first of their kind ever reported, include the mean and variance for the PM recruiting period, the half period of the slow waves, the delay between the slow wave and the spike, and the amplitude of the filtered spike and slow wave. They show the constancy of the period measures inter and intra seizures for the same patient and the higher variability of the amplitude measures.

Preliminary results correlating pairs of the detection parameters are also presented for three patients. The automated detection and quantification of PM seizures, using the present system, are critically brought to a focus.


viii














CHAPTER I
LITERATURE SURVEY

Two research methods have been applied to automated

electroencephalogram (EEG) studies: spectral analysis and time domain analysis. It is the purpose of this chapter to survey the basic different techniques and assumptions involved and to present a better picture of the advantages and limitations of each method. Our attention will be mainly focused on techniques used or related to detection of pathological paroxysmal events in the EEG, and the literature referenced herein denotes this emphasis.


Spectral Analysis

Before addressing this subject, let us first summarize the general assumptions made about the EEG that validate the application of the technique. The theory behind the frequency domain approach using a nonparametric model, as in conventional power spectral analysis, handles the EEG signal as a stochastic process. The statistical properties of the process essentially influence the analytical results. One major difficulty is exactly the different opinions about the stationarity and Gaussian behavior of the EEG process which are prerequisites to carry out spectral analysis and to use the power spectrum as a sufficient









descriptor of the EEG parameters. At the present time this is a very hot topic where one can read reports that show the short time stationarity of the EEG for sequences below 20 seconds for a probability of error of 10 percent (Cohen & Sances, 1977; Kawabata, 1973; Saltzberg, 1972). However, the work of Elul (1967, 1969) and Dumermuth (1968) points out the nonstationary behavior of EEG sequences as short as

4 seconds. Another important characteristic, albeit less addressed, is the Gaussianity of the EEG. The work of Elul (1967, 1969) and McEwen and Andersen (1975)'suggested that the behavior of the EEG followed a Gaussian distribution 32 to 66 percent of the time depending upon the behavioral state of the subject (active mental task to relaxed state, respectively). It also displayed a spatial distribution with closer Gaussian characteristics in the occipital leads. Some of the discrepancies that are reported in the literature can be explained by the different sampling rates used in the A/D conversion, since oversampling may distort the local statistical properties of the digital waveforms (Persson, 1974). Another reason, and maybe more plausible, just demonstrates the variability of the EEG with subject and behavioral state.

In practice the stationarity requirement can be loosened to stationarity during the observation period, and if the process departs slightly from Gaussianity, ancillary parameters like skewness and kurtosis could be employed along with spectral analysis. If stationarity holds, but









the segments are highly non-Gaussian, higher order statistics as bispectra (Dumermuth et al., 1970) could be needed.

Undoubtedly, the early work on EEG quantification of Grass and Gibbs (1938), Walter and coworkers (1963, 1966, 1967) brought improvement to the field of electroencephalography, which at the time was faced with amplitude measurements of randomlike activity. Maybe more important yet, it brought a consistent analysis technique, well established from other areas with an enormous amount of computational power. After the introduction of the Fast Fourier Transform (FFT) algorithm in 1965 by Cooley and Tukey, this power increased manifold. At this point, however, the means began to obscure the basic constraints of the method.

Let us review then the methods of spectral analysis. One of the basic results is to obtain the power spectrum, i.e., an estimate of the mean square value or average intensity of the EEG as a function of frequency. It displays the decomposition of the total variance into contribution from the individual frequency bands. To obtain the power spectrum one can apply Fourier transform to correlograms (indirect method, Blackman and Tukey, 1958), or take directly the Fourier transform of the data and square its absolute value--periodograms (direct method, Dumermuth & Keller, 1973; Matousek, 1973), or use autoregressive techniques (Gersch, 1970; Mathieu, 1970). After the introduction of the FFT the direct method is by far the most widely used.









To find the periodogram, the FFT of the finite EEG sequence is taken. The finite time series can be thought of as the multiplication of the infinite time series X(t) with a rectangular window function of duration T. In the frequency domain this corresponds to the convolution of the spectrum of X(t) with a sinf/f which introduces finite resolution and leakage in the spectrum of X(t) and therefore affects any spectral quantity extracted from it. The finite resolution and leakage are always coupled together and derive from general relations between the time (duration) and frequency (bandwidth) domain transformations (Thomas, 1969). It is only possible to improve one at expense of' the other. One family of approximation functions that yield the optimum compromise (prolate spheroidal functions) are quite difficult to implement and are seldom used (Temes et al., 1973), so more readily available functions are preferred. The best solution is to deal with each problem separately: use a window (Hammings, Kaiser, Tukey, Barlett, see Childers & Durling, 1975) to smooth the data which will improve side lobe rejection; and increase the record length to improve the resolution. The last requirement can only be accomplished at the expense of longer computation times and is directly constrained by the stationarity of the data. This concept deserves a further explanation because sometimes the increase of the record length, by appending zeros at the end of the data record, is thought to increase the "resolution." As a matter of









fact, the procedure displays more points of the discrete Fourier transform (DFT), and so a better approximation to the Z transform is achieved. However, the Z transform remains the same (as long as the record length is constant), so the initial resolution is kept unchanged.

Another problem encountered is the estimation of the power spectrum. Let us resume the estimation process. To compute the essential statistical properties of a Gaussian random process the more general way is to evaluate the autocorrelation function by ensemble average. The method is computationally expensive since various sample sequences of the process have to be available. If the random process is ergodic (Lee, 1960; Thomas, 1969), then it is correct to compute the autocorrelation function by a time average only over one sequence. There are fewer memory requirements involved, but as the properties of the random process are to be inferred from the ones calculated in the sample sequence, consistent estimators have to be used (i.e., estimators that are unbiased and whose variance decreases with the number of data points). It is very easy to find consistent estimators for the autocorrelation functions (Oppenheim and .Shafex:, 1975). The problem arises when the goal is to estimate the power spectrum. It is not true in general that the Fourier transform of a consistent estimator of the autocorrelation function (periodogram) will produce a good estimate of the power spectrum (Barlett, 1953; Jenkins & Watts, 1969). When an infinite number of









points is used to evaluate the periodogram, very rapid fluctuations are present in the estimate of the spectrum. This fact shows that increasing the number of data points of the observation sequence will not change the statistical properties of the estimator since the individual significance of the data points remains the same. To increase the stability of the spectral estimates, the number of independent observations have to be higher or in some way the statistics of the observation have to be improved. These two points lead to the two main methods of increasing the stability of the estimation--the averaging of periodograms (Barlett, 1953), and the smoothing by means of a window (Welch, 1967).

Let us describe briefly the two methods. The Barlett method averages the periodogram over certain frequency bands. To achieve this the data are divided in k segments; the periodogram is calculated for each segment; and the final estimate is the average of the various periodograms. The procedure leads to a bias estimate, but the variance decreases with k (overlapped segments can be used at expenses of lower independence of individual segments and smaller resolution). The number of points on the power spectrum is decreased by k.

The Welch method windows segments of the data before the periodogram is calculated. Generally the triangular window is used to ensure positive estimates of the power spectrum. The methodology is the same as for the Barlett









method, and Welch was able to show that the variance also decreased with k and the reduction on.resolution was also present. Both methods give similar results, so generally the Barlett method is preferred to save one step (Dumermuth, 1968; Matousek & Petersen, 1973; Hagne et al., 1973).

Although the variance of the estimate can be made arbitrarily small, there is a trade-off for resolution. Therefore, if an unknown spectrum is going to be estimated, great care must be exercised not to miss peaks in the power spectrum and at the same time trust the peaks displayed.

In EEG the modified periodogram as an estimator of the power spectrum has been widely used. One of the pioneering works was done at UCLA to investigate the EEG activity of astronaut candidates by D. O. Walter and coworkers (Walter, 1963; Walter, Rhodes, Brown & Adey, 1966; Walter, Kado, Rhodes & Adey, 1967; Walter, Rhodes & Adey, 1967). Also, Dumermuth and coworkers in Switzerland (Dumermuth, Huber, Kleiner & Gasser, 1970; Dumermuth, 1968) use extensively this technique. It has been applied in automated sleep scoring (Walter et al., 1967; Caille, 1967; Rosadini et al., 1968), age-dependent EEG changes (Hagne et al., 1973; Matousek & Petersen, 1973), schizophrenia (Giannitrapini & Kayton, 1974; Etevenon et al., 1976), studies of EEG in twins (Dumermuth, 1968), studies of EEG background activity (Walter et al., 1966; Zetterberg, 1969; Gevins et al., 1975), brain lesions (Walter et al., 1967), and also drug evaluation (Matejcek & Devos, 1976; K�nkel et al., 1976).









Sometimes the power spectrum is not the only parameter used. Dumermuth et al. (1972) uses the bispectrum, that is, the Fourier transform of the second order autocorrelation function R(tl, t2, tl+t2) to investigate coupling between EEG frequencies. Incidentally, the bispectrum analysis shows that, unless for the ac and 8 frequency bands, the function is practically zero, as would be the case for a Gaussian random process. The coherence spectrum

--ratio of the square of the cross spectrum over the spectra of the individual waveforms--is also used to investigate correlation between two EEG channels (Dumermuth et al., 1972; Walter et al., 1967).

The most bothersome question in the application of the periodogram as an estimator is the fact that there are no "best criteria" to determine the combination, window duration-overlap for a particular data sequence. That is one of the reasons why other more consistent methods (in the sense that an error criterion can be defined and leads to a minimization), as the autoregressive (AR) and autoregressive moving average (ARMA), have been recently introduced (Fenwick et al., 1967; Isaksson, 1975; Gersch & Sharp, 1973). The assumption behind their application is that the EEG sequence selected is a sample from a stationary time series. Therefore, it can be modeled as the output of a linear system (if transients are excluded) with a white noise input. The output can then be interpreted as the linear superposition of the natural modes of the system.









The eigenvalues extracted from the parametric time series model of the EEG are the characteristic frequencies and their associated damping factors. The damping reflects the extent to which the EEG will exhibit an oscillatory or random appearance. Unlike nonparametric (conventional) spectra analysis, the relative dominance of the frequencies in the EEG can be associated with the ordering of the magnitudes of the eigenvalues.

In the AR model, the linear system transfer function is approximated by an all-pole function. The two problems are the determination of the filter poles location and the order of the approximation polynomial. There are three main minimization procedures to fit the AR model to the data: one evaluates the filter coefficients as the maximum likelihood estimate when the input to the linear system is white Gaussian noise and the output is the data sequence available (maximum likelihood method). Another evaluates the filter coefficients in such a way that the mean square error between the next sample and the predicted one, given the data sequence, is minimized (linear prediction). Finally, the other calculates the filter poles in such a manner that the estimated values of the sequence maximize the entropy of the autocorrelation function (maximum entropy). The three methods have been developed under different constraints, but recently van den Bos (1971) and Smylie et al. (1973) proved their equivalence. It is also interesting to note that all the methods arrive at the same









matrix equation involving the autocorrelation function (Yule Walker equation (YW)). To estimate the filter coefficients, the YW equation can be solved. Then the autocorrelation functions for various lags have to be computed and a matrix inversion performed. Algorithms due to Levinson (1947) or Durbin (1960) are generally preferred to solve it recursively.

A technique due to Burg (1967) suggests another estimation of the coefficients that does not require prior estimate of the autocorrelation function. It fits successively higher order prediction error operators to the input data by convolving the filter in both forward and backward direction. The square of the two error series are added to obtain the error power,and the filter coefficients are determined by a minimization procedure. A recursion relation is also available (Burg, 1967, 1972; Anderson, 1974). Actually the two different techniques (YW method and Burg) use the data in two different ways. The YW assumes that the data is zero beyond the limits of the observation window. The Burg technique extends the estimation of the autocovariance coefficients beyond the initial number of points in such a way that the entropy of the autocovariance function is maximized at each step. As can be expected, the two techniques have quite different properties. The estimator by the YW method has the attractive property that its mean square error is generally smaller than other estimators (Jenkins & Watts, 1969). However, the estimates are









very sensitive to rounding (Box & Jenkins, 1970) mainly for random processes that display peaking power spectrum, which means that the resolution obtained is not always enough. This is to be expected since the YW technique effectively windows the data. The Burg technique does not display this shortcoming of lack of resolution. It has been shown (Pusey, 1975) that it can resolve two tones arbitrarily close if the S/N ratio is high enough. However, the variance of the estimator is larger than for the YW and does not decrease to zero monotonically.

The correct identification of the order of the AR

model that approximates the data is vital in the computation of the power spectrum (Ulrich & Bishop, 1975). The criterion generally used is Akaike's Final Prediction error (FPE) that is defined as the mean square prediction error (Akaike, 1969, 1970). The YW estimate of the order of the process using this criterion tends to be conservative but with a small variance. The Burg estimate of the order displays a large variance, so generally some upper bound must be imposed in the search. Another approach is to use the first minimum in the estimated error (Ulrich & Bishop, 1975).

While the AR model is an all-pole approximation to the random process, the ARMA model is a pole-zero approximation. Computationally it is the more expensive (in time and memory dimensions) and more difficult to implement, but the two techniques for AR computations could be modified









for this more general case (Treitel et al., 1977). However, as an infinite AR process can approximate any ARMA process, this property of the AR model is preferred. The FPE criteria to determine the order of the AR model can still be used, but there is a tendency to overestimate the order (Ulrich & Bishop, 1975).

After briefly reviewing the three approximation models

(MA, AR, ARMA) to estimate the power spectrum, a question must still be answered. From the sequence of the random process available how should one decide what model to use? This question (identification problem) has not yet been-answered in general, and only in some cases the physical knowledge of the generation process of the data has helped. It is surprising that we have not seen published any work in this direction by the users of these techniques in EEG. On the contrary, the approximation properties of the AR model have been exclusively used. There are reports in the / literature (Treitel et al., 1977) that clearly show that this can lead to inappropriate approximations, which means that there is no single correct technique to calculate the spectrum in the absence of knowledge about the physics of generation.

In EEG the autoregressive model has been used by Fenwick et al. (1969) to predict evoked responses. Pfurtscheller and Haring (1972) used AR models to attempt data compression. Gersch & Sharp (1973) used AR models for multivariate EEG analysis. Wennberg & Zetterberg (1971)









used ARMA models to extract alpha, beta, delta, and theta band intensities for automatic EEG classifications. Mathieu (1970, 1976) used AR models in sleep scoring. Jones (1974) compared the window lag estimation with AR estimator to determine power spectral and coherence functions in the neonate EEGs. Gersch and Yonemoto (1977) compared the AR and ARMA models for the power spectrum estimation of EEG. The same authors (1973) also used parametric AR models to apply the Shannon-Gelfand-Yaglom amount of information measure in sleep scoring.

In epilepsy AR models have been used to-analyze the ictal event. Gersch and Goddard (1970) used the partial coherence among time series to extract information about driving. Tharp (1972) and Tharp and Gersch (1975) use a similar procedure to determine seizure focus. Herolf (1973) and Lopes da Silva et al. (1975) also use an AR model to perform seizure detections by inverse filtering.

Another concern faced in spectral analysis is the presentation of the results. Due to the specific techniques involved, the results need to be further processed to be readily interpreted by the neurologist. The main goals are data reduction and readability. The compressed spectral array of Bickford et al. (1973) has been extensively used and summarizes pretty well the changes of EEG with some external factors (different behavioral states, tracking of alpha waves with light stimuli, hemispheric symmetry, acute slow wave abnormalities). The canonogram









method of Gotman and Gloor (1973) consists of a spatial arrangement of polygons of different sizes related to the ratio of (delta + delta)/(alpha + beta) which is thought to be a good descriptor of localized brain abnormalities. It is considered to be a good descriptor for detection of slow wave abnormalities and asymmetries in the EEG if a preprocessing for gross artifacts in the raw data is performed.

The results of optimum filtering have also been applied to extract certain features from the EEG. One of the earliest techniques was matched filtering (Smith et al., 1969; Zetterberg, 1973; Saltzberg, 1971). A matched filter is the filter that maximizes the signal-to-noise ratio, since it transforms all the available information (energy) of the input signal in a voltage at a specific time T. The prerequisites for its construction or modeling are the a priori knowledge of the waveform shape and the stationarity of the background noise. A matched filter is in fact a correlation detector, and a relatively simple way of implementing digitally one (for a white Gaussian noise) is to select a wave pattern, store it backwards in memory, and perform a correlation with the input (template matching). If the noise is not white, we have to prewhiten it and separate the implementation into two steps: first, divide the Fourier transform of the desired wave pattern by the power spectrum of the noise and second, inverse transform the resultant spectrum to obtain the template that can be









stored in the computer memory. For EEG, prewhitening is a must, since the background activity (noise, if a particular pattern has to be detected) is not white. Matched filtering has been used for spike detection in EEG by Saltzberg (1972), Zetterberg (1973), and more recently by Barlow and Sokolov (1975) and Eftang (1975).

Another result borrowed from communication theory is

inverse filtering. The inverse filter is generally applied to extract information about the arrival times of the individual components of a composite waveform (Childers & Durling, 1975; Robinson, 1967). It is required to know the shape of the waveform and to make the stationarity assumption on the background noise. The filter is nonrealizable (the output is theoretically a delta function), and great care must be taken in the required inversion of the Fourier transform of the waveform not to divide by zero. Inverse filtering also deteriorates the S/N ratio, and a compromise has to be reached between resolution and signal-to-noise ratio.

In EEG inverse filtering is used in a different way.

Barlow and Dubinsky (1976) use inverse filtering to generate the impulse responses of bandreject filters (EEG - power spectrum -* square root + individualize band of interest subtract from uniform spectrum (with amplitude equal to maximum) + IDFT (to get impulse response)). This procedure is highly sensitive to truncation effects, and so poor filters result. Lopes da Silva et al. (1975) use a linear









prediction scheme. He implements the inverse filter of the all-pole approximation model of the EEG and monitors the error between the predicted value and the real data points. Deviations above a prescribed threshold are correlated with nonstationarities of the input EEG data. Very similar techniques are used in EEG adaptative segmentation procedures (Bodestein & Praetorious, 1977) which could eventually lead to transient event detection. A combination of the nonstationary information of the phasic events and the sharpness of the spikes was combined by Birkemeier et al. (1978) to increase the resolution separation of the clusters of epileptic transients and background activity. The system requires settings for each patient and works better in epochs with few spikes (otherwise they may bias the estimation). It is sensitive to artifacts.

Etevenon et al. (1976) use null-phase inverse filtering to deconvolve the EEG and then detect fast activity. His method is equivalent to the one just described (Lopes da Silva), but it is executed in the frequency domain. From the EEG sequence the power spectrum is calculated through the periodogram, and after smoothing and whitening the amplitude spectrum is obtained by evaluating the square root. Then the inverse of the spectrum is computed, multiplied by the Fourier transform of the incoming EEG, and the inverse FFT taken. This signal accentuates sharp transients contained in the EEG, and after threshold detection they can be extracted.









To cope with the EEG nonstationarities, recently there have been reports on Kalman-filtering (Isaksson & Wennberg, 1976). If the stationarity constraints are removed from the noise in the ARMA model, it can be shown that the best fit in the least mean squared sense to the time series is achieved by the Kalman filter (Kalman, 1960; Isaksson, 1975). So, this filter is a generalization of the Wiener filter for nonstationary data and is closely related to autoregressive techniques. It consists basically of the ARMA fit to the time series, but due to the inclusion of a feedback loop with variable gain (Kalman gain) the locations of the poles of the system are allowed to vary. The key parameter in the design is the setting of the Kalman gain since it weighs the new value of the residual signal with its past values and changes accordingly the coefficients of the all-pole filter. The gain controls then the adaptability of the filter. If the gain is set at zero, the Kalman filter is just an ARMA fit for the incoming data and is nonadaptable. If the gain is increased, then we have adaptable properties and the tracking is improved with the gain. One important consequence of the adaptability of the filter is to avoid the smoothing effect present in other spectral methods. Incidentally, by comparing the autocorrelation function obtained by any of the stationary spectral methods with the autocorrelation function estimated from the output of the Kalman filter, some knowledge about the limits of the record length to preserve stationarity









can be inferred. Isaksson and Wennberg (1976) point out that about 90 percent of the records of 20 s are stationary which agrees with some of the previous observations. At the present time, only Isaksson (1975) and Isaksson and Wennberg (1976) have used this technique.


Time Domain Approach


If one can relate the degree of quantization to the

maturity of a field of science, electroencephalography is a newborn. The lack of quantization has two main consequences: the inexistence of objective criteria to characterize the EEG phenomenon that weakens any purely analytical research method (like spectral analysis); the resort to a multitude of soft criteria (i.e., not unique), each based on empirically derived parameter values that try to translate the highly nonlinear way the electroencephalographer reads the EEG.

Visual analysis is a true time domain method of detection of structural features like diffuse and localized change in frequency and voltage pattern, changes in the topographic distribution and in the interhemispheric symmetry, sharp and rhythmic activity, paroxysms and unstable or irregular time course. The basic patterns and clinical EEG features are composed on the following step-by-step procedure: the analysis of the period and amplitude.forms the wave concept that is associated with the gradient to give the simple grapho-element. These can be integrated








in a sequence to produce the complex grapho-elements from which, using superposition, the notion of pattern is acquired. The variability in time and hemispheric location gives rise to the time domain structure and topography of the EEG. The job of the electroencephalographer is to individualize these elements and compare them to his acquired set of "normal activity" in order to make the diagnosis. Of course, the boundaries are quite fuzzy, highly subjective, and not always consistent (Woody, 1968; Rose, 1973).

The techniques are then dependent upon the specific

detection task desired, and no simple overview is possible besides the translation to electronic terms of the decomposition process: analysis of the wave's amplitude in certain frequency ranges, which implies broad bandpass filtering, zero crossing, and threshold analysis. Depending upon the criteria formulated the next step can be the testing of the grapho-elements throughout further processing (sharpness or repetition period, for instance) or testing of a pattern by coincidence logic. What makes the process somewhat erratic is that there is no methodology beyond the extensive comparison with the results obtained by the electroencephalographer and accordingly modify the implementation or the criteria until an agreement is reached.

Due to the diversity of techniques, the detection of abnormal brain activity (spikes) will be emphasized. One of the first criteria to detect spikes was the sharpness









(Buckley et al., 1968; Ktonas, 1970; Walter et al., 1973; Gevins et al., 1975). This was achieved by monitoring the first and second derivatives of the EEG and comparing them with a fixed threshold set for each patient. The parameter was found generally unsatisfactory since differentiation increases the energy of the incoming signal at high frequencies (i.e., extends the bandwidth) and the detection system becomes very sensitive to muscle artifacts. The same basic idea was further improved by Carrie (1972a, 1972b, 1972). He established a moving threshold set by background activity. Although the system was still sensitive to high frequencies, since they biased the threshold, he reported better results. Gevins et al. (1975, 1976) also used the curvature parameter (second derivative), but to improve the system performance the duration and frequency of occurrence are also introduced in the detection criteria. The threshold is automatically set for each patient by an empirical algorithm.

A more complex model of abnormal spikes which included different slopes for the leading and trailing edges of the spike, plus a parameter related to the time it takes the wave to reach maximum slope, was introduced by Ktonas and Smith (1974), and it seems to describe fairly well spike activity. Smith (1974) used some of these parameters to implement a spike detector that gave good agreement without adjustment of detector thresholds. Basically, it consists of a set of gated monostables with "on" times related to









the leading edge first derivative (negative excursion), sharpness of the apex, and trailing edge first derivative (positive excursion). The system requires fairly high sampling rates and is somewhat sensitive to the amplitude of the incoming signal and to muscle artifact, although in a smaller degree than the systems that computed the second derivative of the EEG.

Another detection scheme uses the amplitude-frequency characteristics of the background activity and of the spikes to define detection boundaries in a plane. It is a modified scheme of the period amplitude-analysis of Leader et al. (1967) and Carrie and Frost (1971). Ma et al. (1977) used it to establish optimum decision boundaries that turn out to be nonlinear to accommodate the dependence of amplitude threshold with duration. It is necessary to use each patient's background activity and an average value taken from a population of subjects to estimate the boundary (assuming the clusters of normal and abnormal activity are jointly Gaussian distribution with equal a priori probabilities). The results seem promising but are dependent on the availability of the sets and are computationally complicated and expensive (in time and memory dimensions). Harner and Ostergen (1976) also used a similar approach called sequential analysis to display the amplitudeduration of the EEG but preserving the time information. His methods show the clustering of paroxysmal spike activity and some patterns as spike and wave. It is









possible to choose between the display of half or full waves and have a better qualitative view of the rising and falling phase of spike and wave activity. At this time, however, the system is only qualitative (Harner, 1973) since the definition of boundaries for spikes or spike and wave complexes need medium computers and more resolving power. One important theoretical defect of amplitudeduration techniques, still not solved, concerns the mixing of two frequencies having similar amplitudes.

Pattern recognition was also applied to the detection of paroxysmal events in EEG (Serafini, 1973; Viglioni, 1974). The theoretical method for the determination of the relevant parameters by performing data reduction (linear principal component analysis (Larsen, 1969) and nonlinear homeomorphic procedures (Shepard, 1966)) have hardly been applied to the EEG (Gevins et al., 1975). The parameters chosen are once again few in number and related to visual analysis: amplitude and the average value of the waves, number of zero crossings and mean value of zero crossings. The experimental results show that the criteria are satisfactory, but it requires a training set, is critically dependent upon the length of the normalization interval, and requires a fairly large number of decomposition (orthonormal) functions. Following the same line of pattern recognition Matejcek and Schenk (1974), Remond and Renault (1972), and Schenk (1974, 1976) applied a vectorial iteration technique to decompose the EEG. First, the maxima and minima









of the envelope of waveform are estimated, and the higher order component is taken as the mean.value; the second step is an iteration procedure and uses the result of the preceding analysis. The process is repeated until a featureless waveform is obtained. With these wave components the half waves analysis is used to extract further information. The appealing property of this method is the relatively small computation involved (compared to the FFT) and the strict resemblance with the visual (pattern) analysis.

Gotman and Gloor (1976) describe and evaluate a set of parameters to describe the EEG at the waveform level. The technique can therefore recognize phasic interictal events in the EEG. Its main application is to generate information about epileptic focus and degree of abnormality of a particular record. No mention is made on its use in the detection and quantification of generalized seizures. The other work reviewed fell in one of the previously described methods. Vera and Blume (1978) use the derivative method to analyze on line 16 channels of EEG. Chick et al. (1976) use a scheme similar to Smith (1974).

As far as petit mal (PM) activity is concerned, Jestico et al. (1976) use a bandpass filter 2-4 Hz to detect the slow wave component and measure the duration of the paroxysm. Kaiser (1976) used the duration of the spike and of the slow wave monitored at a certain voltage level to detect the PM activity. In a PDP-12 Ehrenberg and Penry (1976) used zero crossing information and a measure of









integrated amplitude from a combination of 4 EEG channels to detect PM activity. The system stores the duration and time of occurrence of the seizure. The overall agreement, consensus versus machine, is 85 percent. It is, however, interesting to note that in the paper's extensive discussion, no mention is made on artifacts that may cause potential problems like chewing and body movements, which suggests that the investigators had available rather clean data. The system is reported to be sensitive to slow wave sleep. Carrie and Frost (1977) also described a spike and wave detector. It is composed of a spike detector, using the sharpness criteria (Carrie, 1972a), an EMG detector and an information of the amplitude of the background activity (Carrie, 1972b). One channel is analyzed on line,and the system stores the duration of the paroxism and its time of occurrence. The agreement is very high for seizures greater than 3 sec (85 percent) but drops off to 25 percent for Sz between 1-3 sec. The patients were reported to have well-defined PM paroxisms and were free of medication. From the EEG data available to us it seems that the large amount of high energy artifacts that resemble the PM pattern when the patients are in an unrestrained environment dictates the use of more powerful pattern recognition algorithms.

Johnson (1978) implemented in a microcomputer a PM

detector based on the repetition properties of the pattern, i.e., spikes followed by slow waves. He used two analog









filters (22-45 Hz spike, and 1.5-4 Hz slow wave), followed by threshold logic to input the basic elements to the microcomputer memory, where the pattern recognition takes place. The system had no false detects in selected epochs, but was very sensitive to irregularities of the pattern in the middle of the ictal event.


Selection of the Method of Seizure Detection


The requirements put on the analysis method related to the specific problem of detection of paroxismal events are the following:

1) The detection shall be performed in real time in

one channel, using a microcomputer.

2) The detector shall have high resolution capabilities and be insensitive to high energy artifacts.

3) It shall also be able to quantify in detail the

paroxisms.

The computation time constraint is probably enough to make the selected choice of analysis obvious, since FFT algorithms that run real time in simple microcomputers, with workable resolutions, are not known to exist. But even in the affirmative case, it seems that spectral analysis is not tailored to event detection in the EEG because the spectrum produces a smoothing (leakage/resolution). To compensate for it, longer sequences and/or special techniques (parametric spectral analysis) need to be used, which increase the computation time.









After obtaining the spectrum, some type of pattern

recognition must be utilized to judge about the presence of certain frequency components coupled with the event, which incidentally must assume a complete knowledge about the background spectrum and the relations time patternsfrequency patterns. The question arises, why not work with the time patterns to begin with?

Another problem is how can the information from frequency analysis be translated to the clinician who sees time patterns and wants information such as time of occurrence (�l sec), duration, amplitude, etc.?

It seems a much more natural choice to use time domain techniques.

The other technique reviewed is matched filtering, which is the optimum detector to extract patterns from a noisy background, when the noise is stationary and the patterns known. The problem with its application to EEG is the variability of the patterns (around 10 percent, Smith, 1978) and the drastic change in the power of the noise (background activity), which deteriorates the detector performance. Yeo (1975) was able to show that a zero crossing detector, although not optimum, performed better when the patterns were allowed to vary. The false alarm rate of the detector is also independent of the noise power.

The technique which detects nonstationarities in the EEG have some drawbacks besides being computationally









expensive. The inverse filtering can not differentiate among types of nonstationarities. Therefore, a preprocessing or other ancillary methodology needs to be developed. Kalman filtering is quite sensitive to the gain setting. For high gains small changes can be exaggerated, and so one is faced with the problem of calibrating the filter, which is usually done with a control data set (artificially generated). The direct dependence of the gain on the type of data, the dependence of the error signal on the power of the input sequence, and some transient behavior of the system are shortcomings.

It seems that the popularity of frequency domain techniques in EEG detection stems from the availability of standard software packages and a fairly well developed (but often forgotten) mathematical methodology. Up to the present, one of the drawbacks of the time domain approach is the implementation medium (hardware) which requires a full engineering development, not always accessible to the clinicians. However, the present innovation trend in microcomputer systems may very well bring the possibility of standardization through the software implementation of detectors, at low price.

To build an electronic detector where some parameters (amplitude in a prescribed frequency range, zero crossing, sharpness) have to be monitored and decisions made, the omissions created by the poor quantization (definitions) of the EEG process have to be filled. That is the reason why









soft (e.g., nonunique) criteria have to be created and the result of the detection always compared to the EEG scoring by the experts.

The attractiveness of the procedure resides in the small number of assumptions needed on the data and the simple and fast implementation of most of the parameters. On the other hand, there is no theoretical analysis backing it; therefore, the methodology almost exclusively used is trial and error. The process is long and sensitive to errors in the choice of the key parameters or misjudgements of the criteria.

From the time domain techniques known there was some hesitation between employing the rather well-established techniques developed by Smith et al. (1975) to analyze sleep EEG and the ones proposed by Gotman and Gloor (1976) of implementing definitions in the raw EEG. Since the implementation of a completely digital petit mal detector around a microcomputer was, per se, a task which involved quite a few unknown steps, it was decided to use the technique which was best documented. However, it is expected that this work will give quantitative bases for comparing the two different methodologies, with respect to the appropriateness of using prefiltering in the detection schemes of short nonstationarities, like spikes.

Chapter II will be devoted to the design of digital

filters using microcomputers and study in detail the hardware selection of A/D converter number of bits and









computation wordlength to obtain a certain output signal to noise ratio.

In Chapter III the model for the petit mal activity

utilized in the detection will be presented, along with its implementation on a microcomputer. The system's testing will also be explained there.

As this research work is primarily engineering

oriented (a new instrumentation system is designed around a new model of the petit mal activity), the system's evaluation is presented in Chapter IV. Preliminary data demonstrating the high resolution capabilities of the detector and its use in quantifying the petit mal seizure data will also be presented.














CHAPTER II
MICROCOMPUTER BASED DIGITAL FILTER DESIGN


The purpose of this chapter is to analyze the tradeoffs in digital filter implementation using microcomputers and arrive at a comprehensive design procedure. The design approach proceeds from the study of the digital filter noise factor to the choice of a microcomputer wordlength and A/D converter precision, so that a specified output signal to noise ratio could be obtained. This approach is quite general and may be valuable even if future technologies will make practical other implementation media (e.g., bit slice microcomputers).


Preliminary Considerations

For quite some time the EEG research group at the

University of Florida has been developing nonlinear methods for the detection of EEG waveforms. Basically the detectors include bandpass filters followed by zero crossing and threshold analysis of the filtered data to extract information about period, amplitude and number of in-band waves in the raw EEG. The superiority of this detection method for EEG activity has been established when the variability of the patterns is fairly high (greater than 10 percent-Smith, -1978). The bandpass filters have up to the









present been implemented in analog form. The remainder of the pattern recognition algorithm is implemented digitally. Analog filters have the disadvantage of being very sensitive to changes of the component values produced by environment parameters like temperature, humidity, and aging. Although there are design methods that can minimize the sensitivity to component changes (e.g., leap frog), they are more difficult to design since in such structures there is as-ubstantial:number of feedback loops and the change of one filter parameter implies the modification of a large number of filter components. Another problem to which analog filters are sensitive is the tolerance in component values. To design two filters with identical characteristics some or all of the components have to be hand matched. However, this procedure only applies to that particular point in time, since the matched components can have different aging coefficients and so evolve differently in the long run.

The identical filter characteristics are stressed here because, at the present time, a sensitivity analysis which can be applied to the detection of EEG waveforms is not available. However, it is known from experience that very small differences in the filter parameters and/or pattern criteria produce drastic changes in the detection (Smith, 1979). Therefore, the only way similar detection characteristics can be guaranteed between two systems is to match every detection stage.









The substitution of the analog filters by digital ones is also a natural extension of the present instrumentation since the other functions of the pattern recognition algorithm are already digitally implemented. The repeatibility and uniformity of characteristics will be therefore ensured.

The implementation of digital filters could be accomplished basically in two different ways: building special purpose machines to implement the filter algorithm (hardware) or making use of general purpose computers and writing adequate software to accomplish the filtering function. The two techniques possess different properties that are worth comparing. The main advantage of the hardware realization is speed since the processor's architecture is intentionally adapted to the special type of processing, e.g., multiplications and additions (Gold et al., 1971; de Mori et al., 1975). Generally, the processor is microprogrammed and the arithmetic unit is implemented in fast ECL logic. There are some minor modifications to the basic procedure, the use of Read Only Memories to implement the multipliers being the most interesting (Peled & Liu, 1974). However, the development of a special processor is very expensive and implies the availability of specialized laboratories and the work of a diversified group of researchers.

On the other hand, the software implementation of

digital filters can be performed by anyone who masters a computer language as long as the recursion relation is









available. This fact per se has the potential to expand the field of application of digital filter signal processing. This approach is also less expensive since the machine may be a general purpose computer, and so there is no extra cost involved in the new application. The drawback is the computer's fixed architecture which is not adapted to calculate recursion relations.

For a lot of applications the requirements of the implementation can be met with mini-computers and even microcomputers. The principal elements of the requirement set are speed, type of arithmetic, wordlength. Digital algorithms work in digital representations of real world (analog) signals. It is well known (Thomas) that to make a digital representation of an analog signal unique (i.e., the analog signal can be reconstructed again from the digital samples) a maximum frequency must be assumed in the signal spectrum. This is the same as saying that the time domain representation of the signal is restricted to change at less than a prescribed rate, governed by the time/ frequency inverse relationship. The theorem that relates the uniqueness of the digital representation and the sampling frequency is the Nyquist theorem, and it imposes a lower bound on the sampling frequency (sampling frequency equal to two fM). This theorem assumes two impossibilities: first, that the signal spectra are frequency band limited, and second, that the past and future history of the signals are completely available for reconstructing the analog









signal. Here we will not discuss the validity of the hypothesis but will acknowledge the fact that the signal's digital representation is an approximation. To describe sampled waveforms in the time domain a sampling frequency higher than the Nyquist rate should be utilized. Therefore, for real time processing a sampling frequency between 200 and 300 Hz seems adequate for most applications (Smith, 1979), which means, in the worst case, that the computation time per sample must be less than 3.34 ms. An analysis of the clock frequencies and the instruction cycles of today's microcomputers shows that hundreds of operations can be performed in this interval. It seems a comfortable margin when one compares this number with the apparent simplicity of the recursion algorithm--a few multiplications and additions. "Apparent" is stressed because we are generally. led fo think in nterm.offloating point arithmetic. It is a good exercise to estimate the enormous number of operations needed to perform a floating point operation when using numbers greater than one as sole representations. It turns out that the computation time becomes prohibitive if floating point is utilized. There are other types of arithmetic, like the block floating point (Oppenheim, 1970), which do not seem to bring any advantage for our application.

The most severe limitation in the use of fixed point arithmetic is the small dynamic range, since the maximum representable number is 2b, where b+l is the number of bits








in the processor wordlength. The wordlength is also coupled to the precision of the representation because the numbers that represent the constants (and signals) must be quantized to fit the wordlength. For instance, if an 8 bit processor is used, the constants are represented only by two hexadecimal digits.

The choice of software implementation of digital filters in microcomputers imposes stringent constraints which must be carefully examined to ensure that the analog input signal to noise ratio is not degraded. Nevertheless, the use of microcomputers is thought a good choice due to their cost, size, availability, and the ease with which the filtering function is actually performed, requiring primarily software knowledge. In this specific application, as rather sophisticated pattern recognition algorithms will be necessary, the microcomputer will also be time shared, to accomplish these functions.


Design Criteria

The design of digital filters can be broadly divided

in two phases. The first is related with the determination of the filter algorithm and the second with the implementation of the recursion relation. Generally they are taken independently since the type of problems encountered are quite different. In the design of the filter algorithm a machine of infinite wordlength is assumed. The goal is to arrive at a recursion relation that better fits the









filter's frequency (or time) specifications. In the second phase the objective is to choose filter implementations which optimize, in some sense, the finite wordlength effects of any practical processor. The most important problems of the finite length effects are the finite dynamic range of the computation, which may cause overflows, and the finite precision of the constants, arithmetic, and input data, which produces error that may degrade the signal to noise ratio.

It turns out that the two design phases are not completely independent,as will be shown. The microcomputer implementation is expected to be very sensitive to the above-mentioned parameters since the arithmetic must be fixed point (small dynamic range which increases the probability of overflow) and the wordlength is relatively small, giving a heavier weight to the finite effect errors (also called �roundoff: errors). For this reason it was thought convenient not to separate the two design phases in order to have a better perspective of the interactions between a specific recursion relation and its implementation.

As various routes may be taken for digital filter

design, a criterion to compare different design procedures (hence different implementations) is necessary. Here design procedure means selection of appropriate transformation methods to arrive at the algorithm for the filter transfer function, with maximum simplicity in terms of









number of operations, providing at the same time good overflow and noise properties.

To design a filter with a specific output signal to noise ratio using the minimum requirements of computation wordlength and processing time, the following factors need to be analyzed:

1) Filter transfer function

2) Filter internal magnification

3) Noise characteristics of filter topology

4) Processing speed.

The problem as enunciated is relatively different from the design procedure commonly found in the literature, since there the optimization is studied with respect to only one parameter (most generally to sensitivity to roundoff), neglecting any other considerations. It turns out that the optimum structures possess a much higher number of multipliers which will mean slower computation time in our application. Examples are as follows: The synthesis of infinite impulse response filters (IIR) with low roundoff noise based on state space formulations has been presented by Hwang (1976) and Mullis and Roberts (1976). Their structures have N2 more multipliers than the canonical structures, where N is the filter order. Another example will be the structure proposed by Barnes et al. (1977), which is free from overflow oscillations, but requires N+1 more multipliers than the canonical structures. Multiplier extraction was also considered (Szczupack & Mitra, 1975),









but the structures obtained lack the optimum sensitivity characteristics. Another interesting idea is presented in Chang (1978), where the decrease in the roundoff noise is accomplished by feeding back the discarded bits, properly weighed, to the input of the adder following the place where the product is quantized. This procedure doubles the multiplier number. Szczupack:and Mitra (1978) propose the reduction of the roundoff noise by ensuring the presence of zeros in the noise transfer functions. This procedure leads to zeros that are complex, therefore requiring extra multipliers for its realization. Many more examples could be given, but the picture remains unchanged; decrease of roundoff noise means more multipliers. For a microcomputer implementation of digital filters multiplication is by far the most time-consuming operation, and it is therefore necessary to minimize its use. It seems appropriate to say that for microcomputer implementation a suboptimal solution would be the best, weighing the effect of the increase in computation time and the decrease in the variance of the output noise. This analysis is not known to exist, so the procedure chosen utilized canonical structures as well as slight variations in their topology (adders as a variable).


Filter Transfer Function


The characteristics of the filters presently used for sleep EEG studies have been obtained through trial and error. Basically the filters are low Q, second order









bandpass filters (Smith, 1978). The present design uses a slightly underdamped frequency response. It is hard to qualify the desirable properties of the filters since there is no general theory of EEG detection. The only possible criteria are to understand the filter function in the detection scheme and hopefully arrive at some rules that will serve as guidelines for filter selection.

The purpose of using EEG filters in sleep studies is to attenuate out-of-band activity to enable further signal processing (e.g., zero-crossing). On the other hand, the filters shall not mask out-of-band activity so that it will look like in-band activity for the rest of the processing algorithm. Every filtering function produces a certain masking, since the filter output is the convolution of the filter's impulse response with the input. However, the weight of the smoothing is controlled by the Q of the filter, hence the use of low Q filters. At present no other characteristics of the filters, like phase distortion or group delay, have been brought into the picture of filter selection (Smith, 1978). The in-band amplitude characteristics have also been neglected due to the wide variability of the amplitude of the EEG. The above-mentioned analysis refers to EEG sleep studies. For the epilepsy application the knowledge is still less quantitative due to less experience. From the study of the petit mal pattern it can be concluded that the fast attenuation characteristics are of paramount importance for the slow wave filter (activity as









high as 5 Hz) since the spike principal component can be as low as 11 Hz, roughly one octave away. Otherwise, the spike energy will degrade the periodic appearance of the slow wave filter output, preventing the use of full cycle detection, which has been considered the best (Smith, 1978).

After this quick analysis it can be said that the

overwhelming filter characteristics are the good out-ofband attenuation and the low Q. The Q is a factor controlled by the filter parameters and not by the filter type. Therefore, a "good" EEG filter shall display fast out-of-band attenuation. With this constraint in mind, the filter type chosen will be the Chebyshev, since it displays the optimum out-of-band attenuation rate for a certain order, when all the zeros are assumed at infinity (Weinberg, 1962). Elliptic filters have similar attenuation characteristics but are more difficult to design due to the proximity of the poles and zeros. Also for a digital filter implementation this fact means complex zeros and subsequently more multiplications.

To design the digital filters and use the present

experience with analog filters it was decided to accomplish the design in the S plane and use one of the mapping rules to the Z domain (impulse invariant or bilinear). It was thought important to have an automated facility to design the filters from the frequency domain filter characteristics, i.e., center frequency, bandwidth, ripple in-band and









out-of-band attenuation rates. The use of Chebyshev polynomial is suited for this goal as shown in Appendix I.

The procedure to determine the Chebyshev lowpass goes as follows:(Principe et al., 1978):

1. From a given ripple factor (E) in the passband,

the lowpass filter poles can be obtained from (1).

2. To determine n, the polynomial order from the

attenuation in dB/OCT, (3) can be used.



21 2k+1)
s = -sin h4 sin( �f) w
k 2 2n

+ j cos h42 cos(21T) (1)


1 1
1+ - + + 1 )n
sin h)2 E E 2

(2)
1 1
1+ + i + 1 + 1 + n
cos hE2 2E





log( E
n = (3)
log(2 + /v)


Lowpass to Bandpass Transformations


After designing the lowpass filter transfer function, the bandpass can be obtained using one of the standard transformations--the narrow-band or the wide-band









(Blinchikoff, 1976). In the narrow-band, the lowpass filter poles are transformed by the relation


w2-w
= 2 1 i �jw0
SBP 2 LP


where w2, w1 are the upper and lower cut-off frequencies and w0 the center frequency. For the wide-band the poles pairs are given by

a>0 a<0


w0 [-+b�j(Y8-a) w0 [- a-b+j(l+a)]



Y 2 2

A = 1---(a - )
4


y y
w0 [-YZ+b�j (Y+a)]


w0 [-a-bj j-a )] o 2 2


y2 B =
2


a =/ A2+B2 +A


22
b A+B -A
2


and the lowpass poles are -a�j. Here the transformation of the poles is stressed since it will avoid polynomial factorization to obtain the bandpass digital filter in a cascade form.

The two transformations possess quite different properties, the most important for this application being the different Q of the poles. Looking closely at (4) it can be seen that the bandpass poles lay on a parallel to the jw


Pair 1 Pair 2


where









axis. As the Q is proportional to the ratio w/a, the higher frequency poles always possess greater Q. For narrow-band filters the difference is small, but it can become quite appreciable for wide-band filters. Hence, the narrow-band does not transform the time characteristics (overshoot, group delay) of the lowpass design (Blinchikoff, 1976). However, it is widely used due to its simplicity.

With the wide-band transformation, the poles of the bandpass filter lay in a straight line from the origin, ensuring that the ratio w/a is constant. The impulse response of the bandpass filter is a time scaled version of the lowpass. The disadvantage of the wide-band is a more tedious design procedure. It will be shown later that the different characteristics of the transformations will be valuable for the control of the frequency response of the digital filter and the finite length effects of the implementation.


Transformations to the Z Plane


Now that the bandpass pole locations are known, it will be seen how the Z plane pole pairs can be obtained. Basically there are two different types of mapping rules from the S to the Z plane. One, the rational transformations, map the entire jw axis onto the unit circle. There are several ways this can be accomplished (a series expansion of eZt), but the lowest order approximation is the bilinear transformation given by









2 z-1
s + (6)
T z+l

The particular type of isomorphism (an infinite length line mapped into a finite line) implies a nonlinear mapping, in the sense that a Az has different correspondence to a Aw, depending on the value of z. As a matter of fact, the transformation follows a tangent rule as can be easily shown (Oppenheim & Shafer, 1975). Therefore, to get the correct frequency characteristics in the Z domain, the S plane filter critical parameters (center frequency, bandwidth) have to be properly prewarped (Childers & Durling, 1975). Nevertheless, a piecewise linear response is mapped onto a piecewise linear response, preserving the boundaries. It is important to point out that the prewarping does not change the nonlinear properties of the transformation, but compensates for it. So a distortion of the phase response of the filter will always be present.

One of the most interesting properties of the bilinear transform is the absence of aliasing. The theoretical explanation is very easily understood. As the entire jw axis is mapped onto the unit circle, the folding frequency (z=-1) corresponds to w=-, and the attenuation of any realizable network shall also be infinitely large. However, from the Z domain point of view the reasoning does not seem explanatory since the Z axis is the same whether the filter is mapped using a rational or a nonrational transformation. In the particular case of a filter, the









responses must "peak" up at the same place in frequency to make any designs useful, and the response is repeated indefinitely at fs intervals (no matter what jw frequency corresponds to fs/2). The answer must be found in the elements that constitute the network in the Z domain and which are dependent upon the transformation used. In the case of the bilinear, there is always at least one zero mapped at z=-l, which sets at this point the amplitude of the frequency response at zero. So the zero is responsible for the good attenuation properties of the bilinear transform near the folding frequency. This observation is worth noting since it will be useful in the design using nonrational mappings.

The best known nonrational transformation is the impulsive invariant (Oppenheim & Shafer, 1975). There are a few slight modifications, and the direct substitution method will be employed here (Childers & Durling, 1975), where


(s-a.) + (z-e-iT). (7)


ai are the S plane filter poles. Due to the periodicity of the exponential function, the transformation is not one to one. The net effect is that each strip of width ws in the S plane will be overlayed onto the unit circle; i.e., the points wl+Kws (K=1,2,.) will all be mapped into the same point as wl. Mathematically, the frequency response of the digital filter H(ejw) is related to the frequency response of the analog filter (Oppenheim & Shafer, 1975) as










H(ejw) = H (j +j i k) (8)
T a T T


Ha(s) is the Laplace transform of the filter impulse response and T the sampling interval. It is clear that only if H(w) is bandlimited to ws/2, (8) will be a reasonable description. This fact excludes the use of the direct substitution to design high pass filters and in general any function which will display appreciable energy at half the sampling frequency. Anyway it can be expected that the attenuation characteristics of the high frequency end of the filters designed with the straight direct substitution method will be worse than if the bilinear was employed. For the case of bandpass filters, the zeros of the S plane transfer function, if not at s=-, can fold back in the bandpass, ruining the design. Therefore, it is a good design procedure not to map the zeros of the S plane transfer function using this transformation.

It was decided to place the zeros independently in the Z domain. As the filter is a bandpass,at least one zero must be placed at z=1 to block the d.c. gain. Taking into consideration the preceding discussion of the effect of the zero at z=-l, it was decided to place the other zero(s) of the transfer function at z=-l to obtain the good attenuation characteristics of the bilinear transform. The other convenient properties of the zeros at z=�l are the









implementation with simple adders (or subtractors) which are fast and do not contribute any roundoff errors.

It may be expected that the Z domain filter characteristics will not display constant gain across the passband, since a linear relation was used to map the poles and now a zero is being placed at w=ws/2. To compensate for this fact, one technique places a different number of zeros at z=l, according to the relation (Childers & Durling, 1975)


l+cos WcT
k = (9)
1-cos WcT


where wc is filter center frequency.

Bearing in mind the discussion of the lowpass to bandpass transformations, it can be expected that the narrowband will compensate in part the asymmetry since the high frequency pole has already a higher Q than the low frequency one. It turns out that the narrowband transformation used with the direct substitution requires one zero at each of the locations. The number of zeros required for the other combinations (i.e., direct substitution with wideband transformation and bilinear) is shown in Table I for second order filters. From the results obtained with the EEG filters (Principe et al., 1979) it can also be concluded that the sensitivity of the passband gain to different location of the filter center frequency is much lower than (9) predicts.

















TABLE I
REQUIRED NUMBER OF ZEROS


Z = 1 Z = -1


Direct substitution 1 1
narrow-band

Direct substitution 2 1
wide-band

Bilinear 2 2









Another conclusion of the analysis which is very

important regards the filter passband gain. In digital filter design the control of the filter midband gain is generally accomplished by properly scaling the filter transfer function. It is suggested that the correct handling of the Z plane filter design may constitute an alternate way to control the midband gain, at least in some cases. An example given in (Principe et al., 1979) is worth mentioning. For the delta filter (0.1-3 Hz, fs=100 Hz), the midband gain was decreased from 878 for the filter designed with the narrowband direct substitution to 87 just by using the wideband transformation (both frequency responses met the specifications).

Let us analyze in general the effect of the zeros at z=�l in the transfer function. For the zero at z=l the numerator takes the form


z-l = ejWT11 = 4 sin2 wT (10)


and for the zero at z=-l


Iz+ll = 4 cos2 wT (11)


It is concluded that the effect of the zero at z=-l has the symmetric effect of the zero at z=l, with respect to fs/2, so whatever conclusion is reached for one will apply for the other in the symmetric region. Fig. la shows the attenuation characteristics of EQ(10),(11). Now suppose















2 wT 4 sin2 w
2


r/2 . r wT
Fig. la. Frequency Response of One Zero


4 wT 16 cos wT
2


16 sin4 wT


Ir/2


7r wT


Fig. lb. Frequency Response of Two Zeros









that instead of one zero there are two. The numerator becomes (Fig. lb)

2 4 wT
z-i = 16 sin F. (12)

The region of the unit circle where the two zeros give smaller magnification is

4 wT .2 wT
16 sin 2r < 4 sin w


or


wT < arc sin 1 - wT < 600. (13)
2 2

It can be said that the wide-band transformation will yield smaller magnification transfer functions when the filter passband falls in the region 00
The design procedure just described has been implemented in a Fortran IV program, presented in Appendix I. The inputs are the frequency domain specifications of center frequency, bandwidth, ripple in-band and out-ofband attenuation rates. The program chooses the filter









order to meet the specifications and gives the values of the S plane bandpass filter poles, the z domain filter poles and the quadratic factors C and D for each second order resonator given by (a cascade implementation is assumed)


C = 2RE(z)
(14)
D =I (zi)+I2(z.).


The number of zeros at each of the points (z=�l) is printed. The frequency response of the filter is also plotted for a quick check on the design.

The above procedures design infinite impulse response (IIR) filters. For EEG applications, where the attenuation characteristics seem to be more important than the linear phase characteristics, the IIR seem to be preferable to the finite impulse response filters (FIR). However, it is worth mentioning that the FIR can be designed to present a linear phase across the passband, which may be important for applications where the phase information of the input will be an important parameter. Another application which may call for FIR is the situation where multi-sampling rates will be used.

One of the great problems in digital filter design, as mentioned earlier, is the lack of independent midband gain control. Therefore, when a narrow-band filter needs to be designed, the gain shall be expected to be high. To









decrease it, scaling can be utilized at expenses of dynamic range, or for some cases an alternate transformation can give smaller gains. The other possibility is to decrease the sampling frequency, making the filter appear wider and therefore lowering the Q. Although for certain areas like speech processing this is not of great practical value, for EEG it is a viable procedure, since the EEG rhythms can be .considered not coupled. The penalty paid is higher computation time as a digital lowpass filtering shall be performed before the reduction of the sampling frequency to avoid aliasing. Peled (1976) has a detailed analysis of the procedure including setting of lowpass corner frequency and new sampling frequency.

The rationale for using lowpass FIR filters is the

following: If decimation is desired (lower sampling frequency at the output), only the samples which will be used need to be computed. In the case of FIR filters, where the output is only a function of the past values of the input, this can be accomplished easily. For IIR filters the present output is a function of past values of the input plus of the output, which means that every point must be computed. The threshold where the FIR filter is preferable to the IIR is given by the ratio of decimation and the difference in filter order to keep similar attenuation characteristics.

An automated procedure to design IIR bandpass

Chebyshev filters has been presented. It was shown that









it is possible to design bandpass filters using the direct substitution to map the filter poles and a technique derived from the bilinear to map the filter zeros. The relations between the design and the implementation are apparent in the choice of integer zeros (to cut computation time and roundoff noise) and in the choice of the transformation, which may help controlling the midband filter magnification.


Finite Length Effects of the Implementation


After obtaining the filter transfer function in the Z domain, the filter algorithm is the inverse Z transform of H(z). For a second order function of the special type which will be used here, H(z) can be written as in (15) and y(nT) as in (16).

(z+l)
H(z) = (z(+ ) (15)
(z2-Cz+D)


Yn = Cyn-l-Dyn-2+Xn-Xn-1 (16)


The filtering will then be accomplished by computing (16) in the microcomputer.

If an infinite wordlength machine is assumed, the

implementation problem is nonexistent. Practically finite wordlengths must be used leading to the fact that almost every digital filter is nonlinear. For this reason the output of the digital filter deviates from what is actually desired. This leads to the study of various ways of









computing the filter recursion relation. As was said in the introduction for EEG applications, fourth order analog bandpass filters were found satisfactory. Following the basic rules explained in the previous section the transfer function for the class of EEG filters can be written as


H(z) = (-1) (z+l)q (17)
(z -C1z+D1)(z -C2z+D2)


where


l1p, qZ2.


There are three basic ways to implement (17). One is called the direct realization and implements the fourth order polynomial directly. The high sensitivity of this realization to the finite length effects of the implementation is well known (Gold & Rader, 1969). The other two are the cascade and the parallel form. For filters with the zeros on the unit circle, the cascade form can be implemented with fewer multipliers (Childers & Durling, 1975). Therefore, it will be the only one studied. The variables which condition the implementation are the type of arithmetic (fixed or floating point), the number representation (sign magnitude, two's complement and one's complement), and the quantization methods (truncation or rounding).

For fixed point arithmetic, the implementation is based on the assumption that the location of the binary point is fixed, so numbers must be aligned before









performing the additions. If two fixed point numbers are added, overflow can occur (Gold & Rader, 1969), and as there is a linear relation between dynamic range and wordlength, the probability of overflow is large. For the fixed point multiplication, overflow can never occur. However, quantization of the true value shall be generally made, since the product of two b-bits numbers is two b-bits long and it is general practice to use a constant wordlength throughout the filter calculations. For floating point representation a positive number F is represented by F=2CM, where M, the mantissa, is a fraction, and c, the characteristic, can be either positive or negative. Quantization of the mantissa is necessary for both the addition and multiplication. Overflow is also theoretically possible, but as there is an exponential relation between wordlength and dynamic range, it can be essentially excluded. It is therefore assumed that floating point is overflow free.

Truncation and rounding are the two forms of quantization. The quantization error is defined by


E = x-Q(x) (18)


where Q(x) is the portion of x, the input signal, retained. The quantization error depends upon the type of number representation used as shown in Fig. 2. In a microcomputer implementation, the two's complement is the natural choice because it is employed in the processor's arithmetic unit.












ROUNDING

Q (x)


x


PR(e) /A


TRUNCATION

Q (x)


PR(e)


1/A


-b
A=2-b , where b+l is register
length.

Fig. 2. Quantization Error


I









Therefore, the following analysis will be restricted to two's complement truncation and rounding. For rounding the error is bounded by (Oppenheim & -Shafer, 1975)

-2-b- )-b


while for truncation it is


-2-b+l 0
(20)

<2-b+lx<0


where b+l is the number of bits of the wordlength. The truncation error is bigger than the roundoff error, but filters realized with truncation need fewer operations, as truncation is readily done in the microcomputer. Filter Internal Magnification


Fixed point arithmetic must be chosen for the implementation of digital filters in today's microcomputers due to computation time constraints. Therefore, one of the serious problems in the implementation phase is the possibility of overflow in the additions. Overflow causes gross errors in the filtered output and even the possibility of sustained oscillations (Ebert et al., 1969).

An important consideration in the design is to ensure that when an overflow, produced by the input, occurs, the filter will recover in a short time. When the recovery is short, overflow propagation is limited and the filter is









said to have a stable forced response (Claasen et al., 1976). It can be proved that the conditions to guarantee stability of the forced response are equivalent to the zero input stability of the system; i.e., the filter poles must lay in a specific region inside the unit circle. For the special case of second order filters there is a result that can be easily determined and will ensure filters with no overflow propagation. Consider the second order filter

(16) with zero input


Yn = Cyn-1-DYn-2. (21)


The roots of the filter must lay inside the unit circle, which implies that the values C and D must lay inside the triangle shown in Fig. 3b. Ignoring roundoff error and assuming two's complement arithmetic, the output of the filter.subject to overflow will be


Yn = f(CYn-1-DYn-2)


where f( * ) is a sawtooth waveform (the characteristic of two's complement arithmetic shown in Fig. 3a).

It is clear that if


I CYn-1-DYn_21<1 (22)


then yn will be correctly interpreted. So a sufficient condition to have filters with no limit cycles (nor propagation of overflow) is






60








2b-1







b-1 x







Fig. 3a. Overflow Characteristics of Two's Complement


Fig. 3b. No Overflow Propagation Region









ICI+IDI

which is shown in Fig. 3b as the square hatched. This condition is very restrictive for most applications; therefore, most of the practical designs will display the undesirable effect of overflow propagation.

Since the overflow is a nonlinearity in the system, it can be expected that various implementations (different ways of calculating the recursion relation) will display different overflow properties. The parameters one can choose to control the overflow are special type of adders, scaling, and exploring topologic differences in the structures.

When the result of an addition is bigger than the

register length in two's complement representation, there is an abrupt change in sign. It has been shown (Fettweis & Meerkitter, 1972) that at least for the class of wave digital filters, saturation arithmetic allows for the absence of parasitic oscillations. Here saturation arithmetic means the type that holds the signal at maximum level when an overflow occurs. This implies that overflow must be monitored. The relations between the type of saturation arithmetic, distortions at the output and stability are a present area of research (Claasen et al., 1976). No general results are available.

Scaling the signal level is the most general way to

handle overflow. To prevent adder overflow the input, xn









must be scaled so that the output, Yn<1, for all n. There are a number of approaches that can be considered to accomplish this (Oppenheim &'.Shafer, 1975).

As



Yn = hkxn-k (24)
k=O


where hk is the filter response, it is easy to see that



lynl lIhkllxn-kl. Z (maxlxkl) I hkl. (25)
k=O k=O


Therefore, by making maxlxk = 1/ [ lhkl, overflow of yn can k=O

be prevented. This means on the other hand that the zero forming paths of the filter must be multiplied by


k = 1/ _ lhk . Experiments have shown that this scaling
k=0

policy is too pessimistic and does not allow good use of the full dynamic range of the wordlength.

A second approach would be to assume the input sinusoidal, with a frequency equal to the resonant frequency(es) of the filter. This is equivalent to requiring (H( . ) is the filter's frequency response)


IH(eJX)I 2 1 - 1 n (26)

and is accomplished by multiplying the coefficients by k, the scaling constant, so that










a0+ale +a2e
max k 1 (27)
-jx -2jX
l+ble +b2e


where a0, al, a2, bl, b2 are the coefficients of the second order filter. This scaling policy is sometimes too optimistic, that is to say, it may lead to overflow. A third approach uses the frequency domain relation Y(z)=H(z)X(z). The energy of the output signal is k yk, which by k=O

Parsevals relation means


m 2 12x j j
Yk - 2 70 Y(e )y(e- )dX. (28)
k=0

Using Schwartz inequality


2rr 21r.
2 27r 12 j x
k Yk 0 (f H(e )H(e )dl(O X(e3)X(e )dX)
k=0


2 2 rr -jx
S xk0 H(ej )H(e )dX. (29)
k=0


Therefore, scaling constants K may be chosen satisfying


0 k2 H(e j)H(e )dX z 1. (30)



Again, in some applications this policy would be too optimistic (Gold & Rader, 1969). There is available a general theory, which enables signal modelling by constraining the input norms (Jackson, 1970). For the EEG analysis a










1/f type of spectrum may be an adequate model. However, this study was not pursued due to two main reasons. First, the modelling is subject to some gross approximations, mainly for abnormal EEG. Second, no matter what methodology is used, scaling involves the basic approach of increasing the number of multipliers. In our case, where implementation of bandpass transfer functions were obtained without multipliers in the zero forming paths, scaling means increasing tremendously the computation time, as will be shown quantitatively later.

It was decided to allow for a controlled increase in the computation wordlength instead of scaling the filter transfer function. Hence, the internal magnification analysis serves only as an indication of how many bits shall be allocated above the input wordlength to avoid overflow (each power of two corresponds to one bit). Sinusoidal analysis was employed to obtain the information of the wordlength increase, due to its simplicity. It consisted of calculating, using a computer simulation, the maximum value of the transfer functions from the input to the output of each node in the structure.









It has been shown that scaling.uses most efficiently

the dynamic range of the wordlength for a particular structure (Jackson, 1970). However, scaling is essentially a method of controlling the internal magnification. If a certain .filter needs to be built, in a specific machine and with particular structure, scaling just enables its implementation with a good use of dynamic range. Sometimes this methodology may lead to impractical filters, mainly when microcomputers are used as the implementation medium (DeWar et al., 1978). This motivated the search for structures which would display reduced magnifications. Let us take as an example the canonical structure shown in Fig. 4a and also the structure called feedforward of Fig. 4b. They are the only ones which will be compared in this work. Their big advantage from the microcomputer implementation point of view is the minimum (canonic) number of multipliers. The internal magnification in node 1, G1, is the one which will constrain the choice of the wordlength. As is also known, the zeros may counteract the magnification effect of the poles. In the canonical structure, as the feedback signals are always taken before the zeros are implemented, G1 is independent of the zero placement and number. On the other hand, in the feedforward structure, one of the zero forming paths is introduced before the feedback signals are taken, allowing for decreased gains when the filter poles are close to the zeros, i.e., in our application when the filters are low frequency (zero at z=l) or close to fs/2



































Fig. 4a. Canonic Structure


Fig. 4b. Feedforward Structure









(zero at z=-1). This fact has been experimentally noticed in (Mick, 1975). It may also give a."rule of thumb" for the pairing of zeros and poles in the feedforward structure: the zero closer to filter passband shall be implemented first for reduced magnification. The goal is to bound the maximum magnification by the input-output filter gain. When this is possible, both structures present the same wordlength requirements. However, they may display quite different noise power at the output. Fig's. 5a and b present the structures for fourth order filters designed with the direct substitution, narrow-band, wide-band, and the feedforward implementation. The implementation with the canonic form is pictured in Fig. 5c. Noise Analysis


The effect of truncation (rounding) is apparent in

three main areas: the A/D conversion, the multiplications, and the coefficient quantization. As the phenomenon has the same basic characteristics, its modelling will be overviewed first.

Quantization is a nonlinear operation on the signals, but can be modelled, as a superposition on the signal of a set of noise samples shown in Fig. 6 (Rabiner & Gold, 1975). The quantized samples will be expressed by


x(n) = Q[x(n)] = x(n)+e(n) (31)


where x(n) is the exact sample and e(n) the quantization





e


G1 G2


.5


Fig. 5a. 4th Order Filter. Feedforward Implementaton.


a





e


a


G
3




i


e3


4I


Fig. 5b. 4th Order Filter. Canonic Implementation.


G




e


4th Order Filter. Feedforward Implementation (Wide Design).


e


a


Fig. 5c.





e


G5


Fig. 5d. 4th Order Filter. Canonic Form (1D) with Scaling.

























xn=x (t)
x(n) =x(n) +e (n)


e(n)


Fig. 6. Additive Model for Quantization









error. It is common to make the following assumptions on the additive noise process (Gold & Rader, 1969):

1. The sequence of error samples e(n) is a sample

sequence of a stationary random process.

2. The error sequence is uncorrelated with the

sequence of exact samples x(n).

3. The random variables of the error process are

uncorrelated; i.e., the error is a white noise

process.

4. The probability distribution of the error process

is uniform over the range of quantization error.

It is worth pointing out that the above-mentioned hypotheses are approximations that do fail for special types of signals, the most important being the class of constant inputs. But when the sequence x(n) is a complex signal and the quantization step is small, it gives good results. Therefore, the model presented in Fig. 6 will be used for most of the quantization effects in the filter implementation.

The assumption that the error is signal independent is a good approximation for rounding, but for truncation it is clearly not true, since the sign of the error is always opposite to the sign of the signal (20). However, it is easily shown (Oppenheim & Shafer, 1975) that this effect can be incorporated in the mean of the noise process. For truncation, the mean value me and the variance 2 are
given bye
given by









-b
-2
me
(32)
-2b
a2 = 2
e 12


and for rounding by


me =0
(33)
-2b
2 2 e 12


The probability density function for the error process is shown in Fig. 2. The autocovariance sequence of the error is assumed to be


See(n) = ao6(n) (34)


for both rounding and truncation. The ratio of signal power to noise power is a useful measure of the relative strengths of the signal and the noise. For rounding or truncation the signal to noise ratio is


a2 a2 2b 2
s = (12.2 )a (35)
2 -2b s
ae 2 /12
e


or when expressed with a logarithmic scale


2
SNR = 10 log o ) = 6.02b+10.29-10 log10 (a). (36)
e









When the signals are properly scaled to avoid clipping,

(36) can be written as (Oppenheim & Shafer, 1975)

SNR = 6b-1.24 dB : 6b (37)

which shows clearly the interrelationship between dynamic range and quantization error in any signal processing algorithm. For each bit added to the wordlength, the signal to noise ratio improves approximately 6 dB.

It was stated earlier that the class of constant

inputs needs a special modelling. One case that deserves studying is the zero input condition, since it may arise often in real applications. Theoretically, if x(n) is zero in (16), y(n) will then converge to zero if the filter is assumed stable. It has been observed, however, that in the actual system the output does not always display the theoretical behavior. All components of the filter can only attain a finite number of values since they are quantized. This makes the real filter a finite state machine. An immediate consequence of this is that if the filter output does not converge to zero with zero input, it must become periodic after some finite time. The periodic oscillation is referred to as limit cycle or zero input limit cycle (Rabiner, 1972) and is the prototype of correlation between noise samples. The assumptions underlying Fig. 6 are then not applicable, and the best method for investigating zeroinput stability is the second method of Lyapunov (Liu, 1971). The general analysis is very difficult to carry out, and here only the results will be presented for the









case of two's complement truncation and the canonical second order structure. Parker and Hess (1971) showed that the occurrence of limit cycles can occur in the horizontally hatched region of the triangle shown in Fig. 7. The cross hatched region is the stability region (Claasen, et al., 1976). Simulations on digital computers have shown that no limit cycles occur in the remaining region inside the triangle. Probably more important is to have an idea on the bound of the amplitude of the limit cycle. The absolute bound on the amplitude of a limit cycle of any frequency is given by


, 1
1-cl+lIDI


y 1
n max 4 (1- ) 2


/D
(l-D) I-C-/4D


DO and 2/5 ICI

1
D>O and D(2//D-1))JICI~2/D


1
D>O and ICI.2D(2/D-1)2

(38)


for complex roots (Peled, 1976). This bound is too pessimistic, and so the RMS bound is usually preferred (Sandberg &' Kaiser,: 1972). It is given by


1
1-ICI+D
-1
((- y' 2
(1-D)1-C2/4D


DZO or D>O and

IC >4D2/(1+D)


D>0 and IC1<4D2/(l+D)


(39)


































Fig. 7. Stability Region for Second Order Filter


o
o o


0 0
0


tI 1 f I I I 1 1 I


10 12 14 16 18
Wordlength


Fig. 8. Quantization Error Versus Wordlength Cascade Form
(after Rabiner and Gold)









where p is the period of the oscillation. A few points about limit cycles are worth noting. Filters implemented with rounding possess much smaller stability regions than when implemented with truncation. Filters using floating point arithmetic may possess large amplitude limit cycles. In fixed point arithmetic the limit cycle amplitude is generally small (within the noise floor of the filter). It is a general rule that when the amplitude is high, the source of the oscillation is caused by overflow nonlinearities (Claasen et al., 1976). Each implementation of the same second order structure will display its own stability region, the one presented being just a guideline.

As the study of zero input limit cycles is very easy

to accomplish with the real filter, further discussion will be postponed to the implementation phase.

Coefficient quantization. Usually the coefficients of a digital filter are obtained by a design procedure which assumes very large precision. For practical realizations the coefficients must be quantized to a fixed, small, number of bits. As a consequence, the frequency response of the actual filter deviates from the ideal frequency response. Actually this effect is similar to the effect of tolerances in the analog components.

There are two general approaches to the analysis. The first treats coefficient quantization errors as intrinsically statistical quantities, and the effects of the quantization can be modelled as a stray transfer function









in parallel with the corresponding filter (Rabiner & Gold, 1975). The second approach is to study each individual filter separately and optimize the pole locations by comparing the transfer functions of the filter realized with high coefficient precision and the one obtained with the actual values. Rabiner and Gold present experimental results for the error as a function of the wordlength. The table for cascade realization is shown in Fig. 8. For filters realized as a cascade of second order structures, the normalized error variance is below 10-2 for wordlengths of 16 bits. This is considered a very good practical agreement. The degradation is very steep towards shorter wordlengths, the variance being 8 to 10 bit coefficients. Therefore, 16 bit coefficients are thought necessary for practical designs. The extrapolation of their results for any filter realized as a cascade of second order sections is not adequate, since the grid of possible pole locations inside the unit circle is not constant. The grid is defined by the intersections of concentric circles corresponding to the quantization of r2 and straight lines corresponding to quantization of r cos 6 (standard complex notation is used). The density of pole locations is less in regions close to the real Z axis as can be shown in the following way. Consider a filter with pole pair (L,K) where











(40)
-1 k
w = wT = cos1 k
R 2/;


Assuming the errors small


Ar = r AL + Dr Ak

(41)
S- 2 AL + D Ak
DL ak


and substituting (40) yields


Ar 1 AL
2r
(42)
AL _ Ak
2r2tan 8 2r sin 8


Since AO=tAwR, the error sensitivity is directly proportional to the sampling rate. Furthermore, the second equation shows that error in angle 6 is greater when 8 is small (poles with small imaginary part). This point shall be carefully noted since there is a tendency to believe that higher sampling frequencies merely cause the digital filter to behave more like the corresponding analog filter. This is true only if infinite precision in the computations is assumed. For digital filters, it is therefore convenient to define the wide-band concept in the Z domain, since a wide-band analog filter can correspond to a narrow-band digital filter, if the sampling frequency fs utilized is









higher than the Nyquist rate. Also, the implementation of bandpass filters with low center frequencies are the ones which are most sensitive to quantization effects and so should be the ones closely monitored. Practically this can be accomplished by checking the frequency response of the filters obtained with the truncated coefficient values to see if they meet the.desigfn specifications.

A/D conversion noise. The A/D conversion noise is the uncertainty derived from the use of finite precision to represent the analog signals. The assumption of independent signal and noise allows one to proceed with the noise computations while ignoring the signal. Let h(nT) be the system impulse response and H(Z) the corresponding transfer function. Then the output autocorrelation function R (nT) for the noise e(nT) is


R(k) = y(n-k)y(n)
n=O


= [ h(p)e(n-k-p) 1 h(m)e(n-m) n=O p=O m=O


= ( h()h(m)Rx(k-m-p). - (43)
pm


The variance is obtained for k=0; therefore


a = R (0) = [ h(p)h(m)Rx(m-p). (44)
y y p M









Using the property of the noise autocovariance function expressed by (34)


a2 = 02 1 h2(m) (45)
y em=0


where a2 is given by (33). Using Parseval's relation (44)
e
becomes


a2 =2 j h2 (m) = ea2 H(z)H(z-l)z-ldz (46)
Y em=0e 2j c


where c is taken as the unit circle.

This expression is often easier to compute than the infinite summation and will be extensively used.

The transfer function for the signal and A/D conversion noise are the same. Since bandpass filters will be implemented, and the frequency spectrum of the input noise is white, the bandwidth of the output noise is narrower at the output, yielding effectively a2 A/D conversion noise is not the only source of noise introduced in the computations. As the goal is to determine the signal to noise ratio at the output, the total noise at the output must be evaluated including the contribution of the A/D noise.

The result of (46) implies that the system transfer function is realized without any error. In practice this is not the case, but assuming the A/D conversion noise uncorrelated with the other noise sources, the total output noise can be evaluated by simple addition.









Roundoff noise in the multiplications. It is general practice to quantize the output of the multipliers to keep the same wordlength throughout the filter calculations. Essentially the multiplication roundoff noise is the same process as the A/D noise. However, the placement of the noise sources depends upon the structure used and how the arithmetic is actually performed. This means that, in general, the transfer function for the multiplication roundoff noise does not coincide with the systems transfer function. Fig's 5a and 5c show the placement of the noise sources (el, e2, e3, e4) for the feedforward and canonical structure. If the addition was performed in double precision, there would be only one noise source at the output of the adders, but the computation time would have been increased. Truncation of the result is accomplished by just dropping the 16 least significant bits of the product.

To compute equation (46) the transfer function from the noise sources to the output must be determined, along with the weight a2 of the noise sources. When the compuin
tation wordlength is the same as the input number of bits, there is no question what the weight shall be. However, in this case the computation wordlength is bigger than the input number of bits; hence an analysis was undertaken to see which is the limiting factor. Actually this was a very misleading point in the noise analysis, and so two explanations based in different arguments will be presented: From the point of view of the fixed point arithmetic, before an









addition is performed, the addends must be aligned. If the filter computations are correct, the part of the product retained must be aligned with the input; otherwise, the additions which involve the input will not yield the correct result. Hence, the least significant bit of the part of the produce retained has the same weight of the input, even when the computation wordlength is bigger than the input number of bits. The alternate argument follows the "binary point" across the various shifting operations to yield the correct alignment. This will be explained in Appendix II.

To evaluate the total noise at the filter output, the roundoff noise power produced by each source will be added to the input quantization noise, since it is assumed that the noise sources are uncorrelated. There are three quantities that are important noise parameters: the peak inband noise referred to 1 volt, the A/D converter precision, and a dimensionless number a 2 /l , which is a measure of out in
the noise gain of the system and may be translated into the number of bits of the output that are "noisy" (one bit cor2 2
responds to powers of a /a = 3.98). From this ratio out in
and the square of the filter midband gain G the noise factor K

G2
K 2 2 (47)
2 2in out in









can be defined and enables direct comparisons between structures and designs, since it is independent of the input noise variance. The value KZ1 sets the boundary for the case where the noise created by the digitalization and the calculations will degrade, in a r.m.s. sense, the input (analog) signal to noise ratio. The output signal to noise ratio (peak signal power to r.m.s. noise) can be obtained from (47) through a multiplication by A2la/ where in
A is the input signal amplitude. This definition of S/N ratio seems appropriate for EEG signal processing since the various signals of interest are narrow-band and fall in the filter passband.

The filters being of order four, an exhaustive search to find the best cascading of sections and best pole zero pairing was possible. The Dinap program (Bass et al., 1978) was extensively applied to access the noise (and magnification) properties of different structures. Fig. 9 shows a typical output. In (Balakrishnan, 1979) a detailed explanation of the program and its use is presented.


Practical Considerations


Processing Speed


In the internal magnification section it was said that the filters were going to be implemented with a computation wordlength bigger than the input number of bits. This is not the general way of filter implementation, which scales







e


MAXIMUM MAGNIF:'ICAI ION= 0. 60016E I02 FRE:UtENCY ANt.ALYSIS


CHEIDYSIGEV 1rTV ORDER III'ULS.-E IN'J. IDAnIDPASS
C2, D2 -I-1; CI, MI, --1 ,Lil-J WAVF
FREQUENCY (H) lAti IrUDE(D[I) MAON) t lr.

MAX TMUM MiiAGN IFICArTIO NM O. 22S19DE 0;
FRE(I I)IrICY AblALYS1S CHEYSHIEV 4TIH 1 OR[F.R IMPUL.!SE: I.I' BANIPASS
C2.D2, t1sC, 1,DI.--1 SL.A-OW HAVE
FRFGUENCY (H) MACN ITUDE ( IB) MA(Il TUDEI

MAXIMUI'I HA0C-IIA C OI= O 230093E 02
FREUEtINCY ANAI.YSI

CHEDYSIIEV -11H ORDER IIPULSE INV. DANDPASS
Cp, D;, +1 CI. D . I lUit-I , WAVE
FREGUENCY (H) MA I TUDE ' D ) MlAGtl I TiUDF

MAXIMUM MlAGNIFICATI ON- O 479117F 02


Ni)DE NN!tIRER 4


PHIASIE (D)


NOIIVE NUIIDER 7 PHA.E (D) MODE NUMBER 11 PHIAGE (D)


Fig. 9a. Filter Magnification Analysis Using DINAP


e


e


REAL PART


REAL PART


RIEAL PART


IMAG. PART


IMAO. PART


IMAG. PART








e







NI ISE ,ANALY S I L . ,l t i: i t .j 'AGN ITUDn .g�
-59. 86543 .�


--64. 66954.



-69. 47366 .



-74. 27779.



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-33. O1603. .



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--93. 4942.


--9b 29840.



-103. 10251.



-10/. 90663.

O. 10E-'01


l.L . ,i Fi i ) C, jiPUL, fV.
.': 0 . 1 ( 1 . . . . . . . I . . . . ' . .


if * li M~ w


it 9 �
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O 12L 02 . E 02 o. c8E 02


o. 40E 02
0. 36E 02 FREQUENCY (HTZ)


W r ((:2/W*iH'rINIERAL) = O. 30E-03 VOLTS
FREIU ENCY ANII YSI NJDE NU 1li-IER 16

Fig. 9b. Filter Noise Analysis Using DINAP






e


FREGUENCY ANALYSIS NODE IUN IhiLH


MAGNITUDE
60. 01599 .



54. 01489.



48. 01379.



42. 01270.



36. 01160.



30. 01050.



24. 00940.



18. 00830.


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il� k


16 CIiHE YVSilII.V 41H OIR�L INPUL.LE INV. 6ANDPA'Li
(D. Dl?. +l1 1, Di 1 ].0t WAVE

























It


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o. 1OE-1
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10" 1Iti i S i k L i
i i il il
.k:k* * h t & k . . . . . . . . . . . . . . . . . . .
*t**k****ht*it**t **tta*************
.Qt~RQ*R ~Q+RQtR~Q


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0. J 6E 02


0. 20E 02


O. 24E 02


0. 32E 02 0. 40E 02
o0 2i 02 0. 36E 02
FREGUENCY (I-ITZ)


Fig. 9c. Filter Frequency Response (Slow Wave)









the signals within the filter structure. It has been shown (Jackson, 1970) that scaling uses more efficiently the computation wordlength. The values for the scaling factors Gl, G2, and G3 are obtained from the internal magnification analysis. In the scaling design the zeros can no longer be realized as simple adders (subtracters). To use the full dynamic range of the processor the zeros shall be realized as multipliers, increasing the required number from 4 (Fig. 5c) to 9 (Fig. 5d). In a microcomputer implementation this increase slows down drastically the computation, because the multiplication is by far the most time consuming operation. To save computation time, the multiplications can be approximated by shift operations (Oppenheim & Shafer, 1975), but it defeats the purpose of the design procedure. Even in this case, the network complexity increases appreciably (5 more operations per cycle). It can be concluded that scaling better uses the dynamic range at expenses of longer computation times. In (Principe et al., 1979) the results were presented for the class of EEG filters which show that with the nonscaling design only one extra bit is needed to obtain the same output signal to noise ratio. Therefore, for the microcomputer implementation the increase in computation time was thought more demanding than the nonoptimum use of dynamic range.

The nonscaling design coupled with a careful filter design enables the implementation of the class of EEG









filters with only 4 multiplications per cycle, allowing sampling frequencies up to 3 KHZ. Signal to Noise Ratio Specification


Now that the output noise can be calculated and the

filter magnification is known, the important step of choosing the hardware to obtain a given output signal to noise ratio can be addressed. From the specification involving the output signal to noise ratio and the degradation produced in the filtering, the input signal to noise ratio can be calculated, which sets the input wordlength. If the analog dynamic range is smaller, an A/D converter that spans the analog dynamic range shall be chosen and a shift left operation up to the requirement of the input wordlength shall be performed. From the internal magnification analysis the increase in wordlength can be determined and added to the input wordlength to set the computation number of bits.

In the present form a 12 bit A/D converter and a 16 bit microcomputer are being utilized, allowing for the implementation of filters with gain of 16 or less. There may be cases where a longer computation register length may be desirable, but on the other hand a 12 bit A/D converter may be excessive for EEG processing, mainly when the data are prerecorded on analog tape. The dynamic range of a Sangamo 3500 is 46 dB at 60"/sec. (manufacturer specifications), which suggests that an 8 bit A/D is sufficient.









However, the usable signal level really depends on the detection scheme used. For example, a sine wave of 30 Hz,

-46 dB below maximum signal, was recognized with a zero crossing detector at the tape slowest speed (15/16"). It also depends on which digital parameters the algorithm uses. In speech processing figures on 20 dB between the smallest signal that is going to be processed and the A/D noise are frequently used (Gold & Rader, 1969).

The deterioration of the input signal to noise ratio

due to the filtering must also be taken into consideration. It was shown (Principe et al., 1979) that for the case of sleep EEG filters, implemented with the nonscaling design, the noise factor of the implementation ranged from 0.45 to

2.14, i.e., yielding in the worst case a degradation of

1 bit. For all these reasons an 8 bit A/D converter is not recommended to represent the EEG data. A 10 bit A/D (dynamic range of 54 dB) is probably a good choice for EEG applications. If the input of 12 bits obtained with the present A/D converter is scaled to 10 bits, filters with internal gains up to 64 could be directly implemented in a 16 bit microcomputer.

Structures which will introduce the lowest noise and at the same time present the smallest magnification (i.e., for which the input-output gain is the limiting factor) are desired. These specifications are in fact contradictory, and the solution is generally a trade-off between increase in wordlength and large signal to noise ratio. There is no









present theory to arrive at the general rule to pair the poles and zeros and to cascade the second order sections to obtain the "best" solution. The following rule is suggested to set the pairing of the poles and zeros and the order of the cascade. From the general analysis (every possible combination of poles and zeros and ordering) the first thing is to check if the greatest magnification is implementable in the choice of the microcomputer and A/D converter. If it is, then just choose the ordering that
2
displays the lowest a ut If. the. maximum increase in . wordlength required is too big, then choose the pairing which is accommodated by the combination and then pick up the ordering which has the lower noise. As the general analysis may not be available, it is thought important to extend the discussion (although heuristically) of the pairing of the poles and zeros and section ordering. For the case of fourth order filters the rules are simple: If the higher Q pole is realized first, then the output signal to noise ratio can be expected higher. To realize the highest possible signal to noise ratio, the higher Q pole shall be paired with the zero further away from its resonant frequency. However, this methodology can lead to very large magnifications (or the possibility of overflow). To obtain a compromise between the magnification and the signal to noise ratio, the higher Q pole shall be paired with the zero closer to its resonant frequency and realized first. There is no advantage in realizing the higher Q pole last,




Full Text
28
soft (e.g., nonunique) criteria have to be created and the
result of the detection always compared to the EEG scoring
by the experts.
The attractiveness of the procedure resides in the
small number of assumptions needed on the data and the
simple and fast implementation of most of the parameters.
On the other hand, there is no theoretical analysis backing
it; therefore, the methodology almost exclusively used is
trial and error. The process is long and sensitive to
errors in the choice of the key parameters or misjudgements
of the criteria.
From the time domain techniques known there was some
hesitation between employing the rather well-established
techniques developed by Smith et al. (1975) to analyze
sleep EEG and the ones proposed by Gotman and Gloor (1976)
of implementing definitions in the raw EEG. Since the im
plementation of a completely digital petit mal detector
around a microcomputer was, per se, a task which involved
quite a few unknown steps, it was decided to use the tech
nique which was best documented. However, it is expected
that this work will give quantitative bases for comparing
the two different methodologies, with respect to the appro
priateness of using prefiltering in the detection schemes
of short nonstationarities, like spikes.
Chapter II will be devoted to the design of digital
filters using microcomputers and study in detail the hard
ware selection of A/D converter number of bits and


305
TITL *MA I NF
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*
MODULE WHICH PERFORMS A FREQ.
*
ANALYSIS IN A SPECIFIC FREQ.
*
RANGE
=S¡
REQUIRES PEAK PROGRAM AMD F ILT
4.
T
PC = 2 1 5A,WSP=FE 40)
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OUTPUT IS A STAIRCASE WAVE WHI

IS PROPCP.T IONAL TO DATA FREQ (
*
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*
OF FREQ. (D/A III.
*
HRATE- HIGH LIMIT FOR PERIOD

'fe
LRATE- LOW '
*
PERIOD STORES PERIOD
*
DETEC FLAG FOR DETEC.
-fe
PWAVE OLD PERIOD
23C 0
V
AORG >2300
foso
MA I N
EQU >FQ8 0
l EF2
AOC
EQU >1EF2
FC06
MASK
EQU > FCO 6
F C 08
DE TEC
EQU >FC08
FC0 A
FERIO
EQU >FCQ A
00 15
HRAT E
E QU >15
0 0 0F
LRATE
EQU >F
23 £0
PEAK
EQU >23E0
FCOC
P WAVE
EQU > FCO C
2300
02E0
L WPI MAIM
2302
FD8 3
2304
02 05
LI 5 >7FFF
2306
7FFF
230 8
C305
MOV 5,8MASK
230 A
FC 06
230 C
0300
LIMI 3
230E
0003
23 10
0207
LI 7 >FE40
2312
FE40
2214
02 03
LI 9 > 21 5 A
2316
21 5A
2318
0407
8LWP 7 GET DATA
231 A
C 0 02
MOV 2.0
231 C
4020
SZC 2MASK > 0
231 E
F C 06
2320
02EO
L WPI >FF 3 A
2322
FF8A
PROGRAM
:h amp.
>/ A I )
CHANG
m*


ro to to m ro to w to to to to r\j to ra to ro to to to m to to ru to tu to to i\> iv ro ra to ro to to w to to ro to to io to t\> ra to f\) io to to
n*O' O' o o> o> it.O' o> at 0101 tJi ui o o o o o o o q *n *n ti *n -n *n ti m m rn m m m ni n¡ o o o o o o o o o r> o o rv r> n n C3 ca u) at cq m
o<.(>NnmA>in'^foomn>ijDO\f>Mo(iin>mO'Olyomn>aiff'f-'iaomm>oso'4>toonm>fflO')>
288
0A43
SLA
3.4
3D03
D I V
3,4
Cl 81
MOV
1 ,6
C 841
SR A
1 ,4
COSI
MOV
1,2
3381
.MPY
1 ,2
GAC2
SLA
2,12
0943
SRL
3,4
E0C2
SOC
2 ,3
6103
S
3. 4
C046
MOV
6,1
0200
LI
0,>C
000c
CACO
SLA
0 ,>c
E0 40
SOC
0,1
0380
RTWP
Cl 84
SMALL
MOV
4 ,6
04C0
CLR
0
4120
SZC
2MASK4,4
F C 26
1616
JNE
CO NT
0200
LI
0 ,4
0004
Cl 06
MOV
6,4
4120
SZC
2MASKS ,4
FC28
16 02
JNE
SHIFT
0200
LI
0,8
0008
0A05
SHIFT
SLA
5,0
04C4
CLR
4
3D03
DIV
3.4
CA 06
SLA
6,0
El 06
SOC
6,4
Cl 81
MOV
1,6
OA 02
SLA
2,0
04 Cl
CLR
1
3C43
DIV
3,1
0 A 06
SLA
6,0
E0 46
SOC
6, 1
C08 1
MOV
1 ,2
0902
SRL
2,0
1002
JMP
CONTI
Cl 06
CO NT
MOV
6 ,4
C081
MOV
1 ,2
3381
CO NT 1
MPY
l 2
61 03
3
3 ,4
0 ACO
SLA
0,>C
E040
sac
0,1
0330
RTWP
END
NO, INC R3 3Y 1 HEX DIG.
PERFORM DIVISION
ALIGN MEAN
VARIANCE IN P.4
OUTPUT TAG
RO WILL BE SHIFT COUNT
-SHIFT i_. 4 POSSIBLE?
NO, REAL MAG.
RO HAS S.L. COUNT
SHIFT L. 3 POSSIBLE?
YES RO HAS S.L. COUNT
SHIFT REMAINDER OF DIVISION
GET MORE DIGITS IN QUOCIENT
FORM EXPANDED WORD
EXPANDED 1/N*SUM(X*X) IN P.4
ALIGN MEAN IN SAME WAY
MEAN IN P.2
X*X IN R2,3
VARIANCE IN P.4
OUTPUT TAG


261
0110
0046
2160
0206
LI
6,ADC
0111
2162
1EF0
0112
0047
2164
04E6
CLR
§>6(6)
SET GAIN TO 1:1
0113
2166
0006
0114
0048
2168
04E6
CLR
§>8(6)
DISABLE AUTO INC MODE
0115
216A
0008
0116
0049
216C
0205
LI
5, MASK
R5 IS MASK FOR CONVERTIO
0117
216E
7FFF
0118
0050
ft
0119
0051
*
SET UP
OF IMS 9901 AS A TIMER
0120
0052
ft
0121
0053
2170
0200
LI
12,>100
R12 HAS ADDR CF 9901
0122
2172
0100
0123
0054
2174
1E00
SBZ
0
ENABLE INTERRUPT
0124
CC55
2176
1D03
SBO
3
PRIORITY SET TO 3
0125
0056
2178
0300
LIMI
3
SET INT MASK
0126
217A
0003
0127
0057
217C
0200
LI
0,3
9901 FOR IMMEDIATE INT
0128
217E
CC03
0129
0058
2180
33CO
LOCK
0,15
0130
0059
ft
0131
0060
2182
1CFF
JMP
$
0132
0061
2184
1000
NOP
WAIT FOR INTERRUPT
0133
0062
2186
4985
3ACK
SZC
5,§>C(6)
END OF CONVERSION?
0134
2188
0000
0135
0063
218A
13FD
JEQ
BACK
NO, JUMP BACK
0136
0064
218C
02E0
LWPI
SECND
0137
218E
2100
0138
0065
2190
C29B
MOV
*11,10
R10,RECEIVES DATA POINT
0133
0066
*
0140
0067

CALCULATION CF
1ST RESONATOR
0141
0063
t
THE RECURSION RELATION IS
0142
0069

X1+=-DX2+E+C(X1+E)
0143
0070
ft
X2+=X1+E
0144
0071

Y=X2
0145
0072

REGISTER USED
0146
0073
ft
REGISTER 10 FOR
INPJT £
0147
0074

REGISTER 7 FOR
X1
0148
0075
ft
REGISTER 3 FOR
X2
0149
0076

0150
0077
2192
0743
ABS
3
GET SIGN CF Y
0151
0078
2194
3802
MPY
2,3
-DX2 IN R3 R4
0152
0079
2196
1101
JLT
P0ST1
JUMP IF R3 PCS
0153
0080
2198
0503
NEC
3
IF NEG COM PL R3
0154
0031
219A
ACCA
posh
A
10,3
-DX2+E IN R3
0155
0082
219C
0243
MOV
3,9
SAVE IT IN 39
0156
0083
215E
A1CA
A
10,7
X1+E IN R7
0157
0084
21A0
0007
MOV
7,3
X1+E IN R3
0158
0085
21A2
0747
ABS
7
0159
0086
21A4
3901
MPY
1,7
0160
0087
21A6
1505
JGT
PGST2
0161
CHEBY
PACE 3
0162
RECD
LOG
OBJ
SOURCE STATEMENT
0163
0088
21A8
0A47
SLA
7,4
ALLIGN BINARY POINT
0164
0089
21AA
0908
SRL
8,12
XFER 4 BITS FRCM LOWER REG
0165
0090
21AC
E1C8
SOC
8,7
TO HICHER ORDER REG
0166
0091
21AE
0507
NEG
7
0167
0092
21B0
1003
JMP
P0ST5
0168
0093
21B2
0A47
PCST2
SLA
7,4


319
2000
****
*
****
*
*
*
*
*
*
*
*
*
*
*

*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
TI TL OAT A*
*** ***************** ************** ***
OAT A
*************************************
MODULE THAT FORMATS THE DATA TO BE
PLOTTED BY PLOT*
IT TAKES CARE CF ALL INITIALIZATION
SINCE PLOT IS MADE RELOCATADLE
INPUT PARAMETERS
FD63 0 IF SZ<3 SEC ARE CONSIDERED
NOT ZERO OTHERWISE
FD6A- LAST ADDR OF TAG+2
FCO0 DISPLACEMENT TO TAG OF X DATA
FC02- '* Y DATA
FC18- PLOT TYPE
1 POINTS (FROM X AXIS)
2 HISTOGRAM
3 LINEAR INTERPOLATION
HYSTOGP AM ONLY ALLOWS + INC IN X
DATA IS ASSUMED BEG. AT 2720. ACCORDING
TO FORMAT EXPLAINED IN P.M. SZ DETECTOR
MAX X APPEARS
MAX Y APPEARS
IN FD32
IN FD86
ARE USED WITH TEKT,
FOLLOWING CONSTANTS
DISPLAY SCOPE
FCO 4 (CONS) 300
FC06 (XO) SFF
FC08 (YO) SFF
FC14 (SCALE.) 8FF
FC16 (MAX X.Y) 1400
R12 OF WSP PLOT NEEDS TO BE LOADED
BEGINNING ADDR OF PLOT PLUS 39A
WITH
AORG >2000
0 080
MONI T
SOU
>8 0
FFFF
KEY
EQU
>FFFF
2720
STATS
EQU
>2720
FC 12
MASK
EQU
>FC 1 2
FD68
WDATA
EQU
>FD68
FD 80
WPLOT
E QU
>FD8 0
2200
OUT^C
EQU
>2200
FCOO
AODX
EQU
>FC0 0
FC 02
ADDY
EQU
>FC 02
FC04
CONST
EQU
>FC04
FC 06
CLD X
EQU
>FC0o
F C 08
CLDY
EQU
>Fcoa
611


10
matrix equation involving the autocorrelation function
(Yule Walker equation (YW)). To estimate the filter coef
ficients, the YW equation can be solved. Then the autocor
relation functions for various lags have to be computed and
a matrix inversion performed. Algorithms due to Levinson
(1947) or Durbin (1960) are generally preferred to solve it
recursively.
A technique due to Burg (1967) suggests another esti
mation of the coefficients that does not require prior
estimate of the autocorrelation function. It fits succes
sively higher order prediction error operators to the input
data by convolving the filter in both forward and backward
direction. The square of the two error series are added to
obtain the error power,and the filter coefficients are
determined by a minimization procedure. A recursion rela
tion is also available (Burg, 1967, 1972; Anderson, 1974).
Actually the two different techniques (YW method and Burg)
use the data in two different ways. The YW assumes that
the data is zero beyond the limits of the observation win
dow. The Burg technique extends the estimation of the
autocovariance coefficients beyond the initial number of
points in such a way that the entropy of the autocovariance
function is maximized at each step. As can be expected,
the two techniques have quite different properties. The
estimator by the YW method has the attractive property that
its mean square error is generally smaller than other esti
mators (Jenkins & Watts, 1969). However, the estimates are


274


False
Dectection
y--| in- rmr-T-Ti TT~ -7 -tt-t--g--rr- r r nnrrin
Fig. 49a. Mean and Variance of Repetition Period Versus Time (#7-1)
06 sec 1.4 sec


150 pv
i
1sec.
Fig. 27b. PM Detector Output (Patient #12)
155


307


140
The block diagram of the detector is shown in Fig. 24.
It is composed of two parallel processing channels, one for
the slow wave and another for the spike. In a real time
operation, with a single processor, the computations must
be performed serially. It turns out that these facts (real
time operation and parallel channels) put considerable con
straints on the program articulation since for each input
sample, decisions in each channel must be made (e.g., did
a zero crossing occur?), which implies that the linking
among the program modules may be data dependent.
The goal in the program design, which used the top
down approach, was modularity. Each program module was
associated with a particular function of the detection
algorithm, and care was taken to make the modules as inde
pendent as possible. However, the ideal, one entry point
one output (Tausworthe, 1977) would be achieved with much
higher program complexity. It is considered that a good
compromise between a reasonable increase in processing time
and program modularity was achieved.
A functional description of each module is presented
next.
Initialization of A/D converter, timer (TMS 9901)
to set the sampling frequency, filter coefficients,
special pointers and external references. It also
decides about the periodicity of PM complexes
(beginning of seizure) and outputs flags.
MAIN


253
addr + EH. The board has also available 2, 12 bit DAC
channels (base addr + 0 and + 2).
The TMS 9901 Programmable System Interface chip'
was used as a timer to set sampling frequency. It is
addressed through the CRU (addr 10 0), and it uses the
II
interrupt priority 3. The 9901 needs to be set in the
timing mode with the interrupt enable and the processor
interrupt mask set at three. When the value loaded in
bits 1-12 of the CRU, which is decremented at the clock
frequency over 64 reaches zero, the interrupt is activated.
In the TM 990/101M-1 board interrupt 3 is vectored to the
beginning of memory, where PC is loaded with FFAA. and WSP
11
with FF88 (TMS 9900 Data Manual).
H
The flowchart of the filter program is shown in
Fig. II-2, and it is configured in an endless loop to be
used as a real time filter. Minor modifications were
introduced in this program flow to be used as a subroutine
in the detector (instead of closing the loop, the program
ends with a RTWP instruction).
Implementation of the Filter Algorithm
To accomplish a digital filtering function only addi
tions, multiplications and delays (memory) need to be
implemented. Fig. II-3 presents, for convenience, one sec
tion of the structure used as in the implementation of the
EEG filters. After the topology of the resonator, the next
value x* and x* at the input of the storing elements (state


Ill
For this value of t2 the error is
(t2*-T) sin wt2+t2 sin w(T-t2)
sin wt2+sin w(T-t2)
(53)
Now substituting in our example of the 80 Hz sampling fre
quency and 16 Hz sinusoid the maximum error is 0.33 ms.
As expected, the interpolation decreased the error a lot.
This point brings up the question of "availability" of
information in the digital representation of the signal.
The Nyquist theorem only shows that, if the signal informa
tion is used from the infinite past to the infinite future,
the digital samples possess the total information for wave
form reconstruction. In practice, the assumption is impos
sible, and therefore a certain error must be tolerated.
The practical question is what is the best compromise,
sampling frequency/reconstruction method from the point of
view of accuracy and computation speed, when both quantities
are considered as variables. It was shown that for the
simple case of frequency determination by period measure
ments, the interpolation method was much more accurate than
the simple zero-crossing. However, interpolation is much
more time consuming. For this.particular application where
the arithmetic facilities are scarce, it seems appropriate
to increase the overall digital representation of the wave
by sampling the analog waveforms at a higher rate, and use
fast, easily implementahle detection schemes like -.zero
crossing analysis. The savings are even more apparent when


231
and with similar parameters to set the middle of the
period/amplitude windows and then allow a certain varia
tion. These methods have to be tested before any definite
solution is taken.
Both detectors employed, the slow wave and spike,
worked well with EEG activity. However, the latter is sen
sitive to artifacts. Any sharp transient in the EEG was
detected as a spike, even when it was "step like." This
fact does not validate the initial assumptions and calls
for the inclusion of a more sophisticated pattern recogni
tion in the spike channel. Fig. 50 shows the performance
of the spike filter (downward pulse in channel II) in a
moving artifact epoch. The modification that is proposed
is to employ the spike detector presented in Smith (1974),
comprising requirements in the positive and negative slopes
as well as sharpness measurements. This improvement
coupled with the analysis of two frontal channels to use
the bilateral synchrony of the PM activity will consider--
ably reduce the false positives. As mentioned earlier,
with minor modifications the system can process two chan
nels of information in real time. If the proposed modifi
cation in the spike channel makes the processing time too
long, a simplification on the spike bandpass filter will be
evaluated. It will consist of coupling a second order high
pass filter with a number of zeros at fs/2 such that enough
attenuation is obtained at the higher frequencies. The
rationale is to save computation time (the zeros are easy


64
1/f type of spectrum may be an adequate model. However,
this study was not pursued due to two main reasons. First,
the modelling is subject to some gross approximations,
mainly for abnormal EEG. Second, no matter what methodol
ogy is used, scaling involves the basic approach of in
creasing the number of multipliers. In our case, where
implementation of bandpass transfer functions were obtained
without multipliers in the zero forming paths, scaling
means increasing tremendously the computation time, as
will be shown quantitatively later.
It was decided to allow for a controlled increase in
the computation wordlength instead of scaling the filter
transfer function. Hence, the internal magnification
analysis serves only as an indication of how many bits
shall be allocated above the input wordlength to avoid
overflow (each power of two corresponds to one bit).
Sinusoidal analysis was employed to obtain the information
of the wordlength increase, due to its simplicity. It
consisted of calculating, using a computer simulation,
the maximum value of the transfer functions from the input
to the output of each node in the structure.


MAX I MUM MAGNIFICAUOM 0.6001 ACE 02
FREQUENCY ANALYSIS NOCE NUMRER 4
CHEBYBI1CV 4TH ORDER IMPULSE INV. BANDPASS
ca. 1)2 I-11 Cl, 1)1, -1 FI .on WAVE
FREQUENCY
(Hi MAONII'UDE(DU)
MAGM] ft IDE
PHASE
(D)
REAL
PART
IMAG.
PART
MAX IMUM MAGM1FICAX1 ON
0.SP3195E 02
FREQUENCY ANALYSIS
NODE NUMBER
7
CHEBYSHEV 4TH ORDER U1PUI
ca. Lia. H¡ Cl. 1)1. -1 SLUM
-BE INV BANDPASS
WAVE
FREQUENCY
MAGNITUDE(OB)
MAGNITUDE
PHASE
(D)
HEAL
PART
IMAQ.
PART
MAXI Ml JIT MAONIF i C AT I Oil-
0 2S00H3E 02
FREQUENCY ANALYSIS
NODE NUMBER
11
CHEBYSHEV 11H ORDER IMPULSE INV. BANDPASS
Ca. 1)2, +1 ¡ C1. D1, 1 5I..UW WAVE
FREQUENCY
(H) MAGNITUDE'DR)
MAGNITUDE
PHASE
(D)
REAL
PART
IMAG.
PART
MAXIMUM MAGNIFICATION- O 477117F 02
03
cn
Fig. 9a. Filter Magnification Analysis Using DINAP


59
said to have a stable forced response (Claasen et al.,
1976). It can be proved that the conditions to guarantee
stability of the forced response are equivalent to the zero
input stability of the system; i.e., the filter poles must
lay in a specific region inside the unit circle. For the
special case of second order filters there is a result that
can be easily determined and will ensure filters with no
overflow propagation. Consider the second order filter
(16) with zero input
(21)
Yn = Cyn_!-Dyn_2.
The roots of the filter must lay inside the unit circle,
which implies that the values C and D must lay inside the
triangle shown in Fig. 3b. Ignoring roundoff error and
assuming two's complement arithmetic, the output of the
filter subject to overflow will be
where f( ) is a sawtooth waveform (the characteristic of
two's complement arithmetic shown in Fig. 3a).
It is clear that if
cyn-rDyn-21 (22)
then yn will be correctly interpreted. So a sufficient
condition to have filters with no limit cycles (nor
propagation of overflow) is


294
2654
0280
Cl
13.SZMIN
INC RESPECTIVE SZ COUNT
2696
0200
2698
1 503
JGT
CO NT
269 A
0 5A0
I NC
3LES33
SZ<3
269 C
FC2A
269E
1032
JMP
CUT
26A 0
0 280
CO NT
Cl
13,TEN
26A2
0960
26A4
1503
JGT
aiG
26A6
05A0
INC
2LES10
3 26A8
FC2C
2 6A A
10 02
JMP
STA
26 AC
0 5 AC
BIG
INC
2GRT 10
3Z> 1 0
2 6AE
FC2E
READY FOR TOTALS
2 63 0
05A0
STA
INC
FLAG
2662
FC22
-
2634
0420
5LWP
3STAT1
R.RATE
2666
FCOE
2 638
C360
*
MOV
2ST ATI. 13
2 63 A
FCOE
2 6 SC
C.FAD
MOV
221 13) *14+
MEAN
263E
0002
26C0
CFAO
MOV
38(13)*414+
VARIAMCE
26C2
0008
1/2 PERIOD OF S.W.
26C4
0420
BLWP
3STAT2
26C6
FC 12
26C8
C360
MOV
2STAT2,13
2 6CA
FC 12
26CC
CFAD
MOV
£21 13) 4 14+
26CE
0002
2600
CFAO
MOV
23(13),414+
2602
0008
2604
0420
OLWP
3STAT3
DELAY SPIKE S.W.
2606
FC 16
2608
C360
MOV
2STAT3,13
2 60 A
FC 1 6
2 6DC
CFAO
MOV
32( 13) ,414+
26DE
0 0 02
26F. 0
CFAD
MOV
38(13),414+
26E2
0 0 08
S.W. AMPLITUDE
2cE4
0420
BLWP
3STAT4
2 6E6
FC IA
26E8
C360
MOV
2STAT4, 13
2 6E A
FC 1A
26EC
CFAO
MOV
32( 13) ,4 14 +
2 6EE
0002
2 6F 0
CFAD
>
a
y
38(13),414+
26F2
0008
SPIKE AMPLITUDE
2 6F4
0420
3L WP
aSTAT5
2 6F6
FC IE
26F3
C3 60
MOV
2STAT5,13
26FA
FC IE
2 6FC
CFAD
MOV
22( 13) ,414 +
26FE
0002
2 70 C
CFAD
MOV
38(13),414+
2702
0008
2704
02 00
CUT
LI
13,>FFFF
OUTPUT SEPARATION TAG
2706
FFFF
270 8
CF 80
MOV
13,414+
2 70 A
C30E
MOV
14.aSZTIM
STORE MEM POINTER
270 C
FC24
2 70E
04 EO
CLP
3FLAG
NO TOTALS FOR STATIS
2710
FC22
2712
C80F
MOV
15,3THRE S
RESTORE S.W. AMP THRES
2714
F C 04
2716
C460
B
2SZCUT
GO TO MAIN
2718
2324
END




80
= /L
0 = wT = cos-"*'
R 2/L
Assuming the errors small
Ar If AL + w Ak
A0 = M AL + M Ak
3L
3k
and substituting (40) yields
Ar =
_ 1
2r
AL
A0 =
AL
Ak
2r tan 0 2r sin 0
(40)
(41)
(42)
Since A0=tAwR, the error sensitivity is directly propor
tional to the sampling rate. Furthermore, the second equa
tion shows that error in angle 0 is greater when 0 is small
(poles with small imaginary part). This point shall be
carefully noted since there is a tendency to believe that
higher sampling frequencies merely cause the digital filter
to behave more like the corresponding analog filter. This
is true only if infinite precision in the computations is
assumed. For digital filters, it is therefore convenient
to define the wide-band concept in the z domain, since a
wide-band analog filter can correspond to a narrow-band
digital filter, if the sampling frequency fs utilized is


236
Hi
ru.

- I
IA
-
CALIBRATION WITH SWEEP SINE 1-7 Hz
inn; nfi
H r*i 'U*
V
r
U L
inr
o
in
iH
^7 ,Uwl
h
uJ^L_J^
4 sec
Fig. 51a. Change of Frequency within Seizure (Patient
#7-1)


167
Subject Profile:
NAME:
last first
AGE: SEX: M F RACE
CLINICAL HISTORY:
START FOOT.:
END FOOT.:
TAPE *:
SUBJECT *:
I
B K other:
MEDICATIONS:
ADDITIONSL INFORMATION/OBSERVATIONS:
Fig. 30. Technical Log Used in the Data Collection


259
period successively reduced. When the computation time is
longer than the time between successive interrupts, the
program is interrupted in the middle of the loop. Due to
the existence of the wait loop at the end of the computa
tions, the width of the time step of the D/A converter
increases approximately to the double of the value pre
viously used. The value loaded in the 9901 that produced
the jump was IB, which corresponds to 277 ys. It is worth
noting that the interrupt handler is also included in the
processing time. The filter implemented needed only the
alignment of one coefficient. One version of the program
is shown next, along with the corresponding interrupt
handler.


REFERENCES
Akaike, H. "Power Spectrum Estimation through Auto
regressive Model Fitting." Ann. Inst. Statist. Math.,
21:407-419, 1969.
Akaike, H. "Statistical Predictor Identification." Ann.
Inst. Statist. Math., 22:203-217, 1970.
Andersen, N. "On the Calculations of Filter Coefficients
for Maximum Entrophy Spectral Analysis." Geophysics,
39:69-72, 1974.
Anderson, R. B. Proving Programs Correct. Wiley, New
York, 1979.
Balakrishnan, S. K. "Digital Filters for EEG Processing,"
Master s Thesis, University of Florida, 1979.
Barlett, M. S. An Introduction to Stochastic Processes
with Special Reference to Methods and Applications.
Cambridge University Press, Cambridge, 1953.
Barlow, J. S., and E. N. Sokolov. "Selective On-Line EEG
Filtering by Means of a Minicomputer." Electroenceph.
Clin. Neurophysiol., 39:208, 1975.
Barlow, J. S., and J. Dubinsky. "Some Computer Approaches
to Continuous Automatic Clinical EEG Monitoring." In
Quantitative Analytic Studies in Epilepsy. Raven
Press, New York, pp. 309-327, 1976.
Barnes, C., Casper, W., and A. Fam. "Minimum Norm Recur
sive Digital Filters That Are Free from Overflow Limit
Cycles." IEEE Trans. Circuits and Systems, CAS-24:569-
574, 1977.
Bass, S. C., Grundmann, J. W., and S. E. Belter. "DINAP
II: A Digital Filter Analysis Program." Purdue
University Technical Report, TR-EE 78-14, March 1978.
Bickford, R. G., Brimm, J., Berger, L., and H. Aung.
"Application of Compressed Spectral Array in Clinical
EEG." In Automation of Clinical Electroencephalog
raphy Raven Press, New York, pp. 55-64, 1973.
333


614 sec
1.39 sec
II I i II I LI
Fig. 41c. Variance R. Period Versus Duration (#5-3)
214


77
Fig. 7. Stability Region for Second Order Filter
u
o
u
M
W
T5
N
H
03
e
h
O
Z
Wordlength
Fig. 8. Quantization Error Versus Wordlength Cascade Form
(after Rabiner and Gold)


218
#12, sometimes with a perfect linear trend (Figs. 44a and
b). For patients #5 and 12 the half period of the slow
waves was insensitive to the repetition rate. The varia
bility on patient #7 did not allow any conclusion (false
detections?). The amplitude of the waves in patients #12,
5-1 and 5-2 decreased with longer repetition periods
(Fig. 45), and for the other no conclusions could be made.
Next, the half period of the waves is going to be used
as X axis. In all the patients the variability increased
with longer half periods (Fig. 46). The slow wave ampli
tude decreases with the half period for patients #12-3 and
5-2. For the others no conclusions could be made.
The spike amplitude and the slow wave amplitude were
also plotted. Only in patient #7-1 do they seem to be
correlated in the sense that high spike amplitudes were
coupled with high slow wave amplitudes (Fig. 47). In the
others no apparent correlation could be perceived. In
summary the trends in the data set are the following:
1) The half periods of the waves remained approximately
constant across seizure duration.
2) The variability of the repetition rate increased
with increased repetition rates.
3) Longer seizures tend to have smaller repetition
rates.
4) The duration of the seizures did not affect the
amplitude of slow waves and spikes.


6
points is used to evaluate the periodogram, very rapid
fluctuations are present in the estimate of the spectrum.
This fact shows that increasing the number of data points
of the observation sequence will not change the statistical
properties of the estimator since the individual signifi
cance of the data points remains the same. To increase the
stability of the spectral estimates, the number of indepen
dent observations have to be higher or in some way the sta
tistics of the observation have to be improved. These two
points lead to the two main methods of increasing the sta
bility of the estimationthe averaging of periodograms
(Barlett, 1953), and the smoothing by means of a window
(Welch, 1967).
Let us describe briefly the two methods. The Barlett
method averages the periodogram over certain frequency
bands. To achieve this the data are divided in k segments;
the periodogram is calculated for each segment; and the
final estimate is the average of the various periodograms.
The procedure leads to a bias estimate, but the variance
decreases with k (overlapped segments can be used at
expenses of lower independence of individual segments and
smaller resolution). The number of points on the power
spectrum is decreased by k.
The Welch method windows segments of the data before
the periodogram is calculated. Generally the triangular
window is used to ensure positive estimates of the power
spectrum. The methodology is the same as for the Barlett


35
in the processor wordlength. The wordlength is also
coupled to the precision of the representation because the
numbers that represent the constants (and signals) must be
quantized to fit the wordlength. For instance, if an 8 bit
processor is used, the constants are represented only by
two hexadecimal digits.
The choice of software implementation of digital fil
ters in microcomputers imposes stringent constraints which
must be carefully examined to ensure that the analog input
signal to noise ratio is not degraded. Nevertheless, the
use of microcomputers is thought a good choice due to their
cost, size, availability, and the ease with which the fil
tering function is actually performed, requiring primarily
software knowledge. In this specific application, as
rather sophisticated pattern recognition algorithms will
be necessary, the microcomputer will also be time shared,
to accomplish these functions.
Design Criteria
The design of digital filters can be broadly divided
in two phases. The first is related with the determination
of the filter algorithm and the second with the implementa
tion of the recursion relation. Generally they are taken
independently since the type of problems encountered are
quite different. In the design of the filter algorithm a
machine of infinite wordlength is assumed. The goal is to
arrive at a recursion relation that better fits the


BIOGRAPHICAL SKETCH
Jose Carlos Santos Carvalho Principe was born April 13,
1950, in Porto, Portugal. He received his bachelor's
degree in Electrical Engineering from the University of
Porto in 1973. He was awarded a Fulbright-ITT scholarship
to pursue graduate studies at the University of Florida,
where he received the Master of Science degree in 1975.
He returned to Portugal and joined the staff of the Elec
trical Engineering Department of the University of Aveiro
as an assistant professor. He was awarded a NATO-Portugal
scholarship to pursue studies towards a Doctor of Philosophy
degree at the University of Florida.
346


334
Birkemeier, W. P., Fontaine, A. B., Celesia, G. G., and
K. M. Ma. "Pattern Recognition Techniques for the
Detection of Epileptic Transients in the EEG." IEEE
Trans. Biomed. Engng., BME-25:213-217, 1978.
Blackman, R. B., and J. S. Tukey. The Measurement of Power
Spectra. Dover Publishing Company, New York, 1958.
Blinchikoff, H. J. Filtering in the Time and Frequency
Domain. John Wiley & Sons, Inc., New York, 1976.
Bodestein, G., and H. M. Praetorious. "Feature Extraction
for the EEG by Adaptative Segmentation." Proceedings
IEEE, 65:642-652, 1977.
Bourne, J. R. "Computer Quantification of EEG Data
Recorded from Renal Patients." Computers and Bio
medical Research, 8:461-473, 1975.
Box, G. E., and G. H. Jenkins. Time Series Analysis:
Forecasting and Control. Holden-Day, San Francisco, .
1970.
Buckley, J. K., Saltzberg, B., and R. G. Health. "Decision
Criteria and Detection Circuitry for Multi-Channel EEG
Correlation." IEEE Region III Convention Record, New
Orleans, 1968.
Burg, J. P. "Maximum Entrophy Spectral Analysis." 37th
Meeting of Soc. of Expo. Geophys., Oklahoma City,
1967.
Burg, J. P. "The Relation between Maximum Entrophy Spec
tral Analysis and Maximum Likelihood Spectra." Geo
physics 37:375-376, 1972.
Caille, E. J. "Apport de 1'analyse Spectral de l'EEG
pendant le Sommeil." Societe Psychol. France, 7,
1967.
Carrie, J. R. G., and J. D. Frost. "A Small Computer
System for EEG Wavelength Amplitude Profile Analysis."
Int. J. Bio-Medical Computing, 2:251-263, 1971.
Carrie, J. R. G. "A Technique for Analyzing Transient EEG
Abnormalities." Electroenceph. Clin. Neurophysiol.,
32:199-201, 1972.
Carrie, J. R. G. "A Hybrid Computer Technique for Detect
ing Sharp EEG Transients." Electroenceph. Clin.
Neurophysiol., 33:336-338, 1972a.


o o o o
0001
0 i.i ME ' FIL. TRO JDB * 1 UOt. > c'iJ68* ? .-¡j U.-1 .1 L- PPINL IRE j L'LH''=M
0003 ." PASSWORD
0004 RDUTE PRINT REMDTF6 '
0005 /v EXEC F0PT6.CS
0006 F DPT. SYS IN PL
000? /'INCLUDE CHEEY1
0008 ./
0009
'bO .
SYSLIE BE
DSN
=SYS
1.FORTLIE?DISP=SHP
0 01 0
LB
DSN
=UF.
3062099.EELIB.PISP=SHR
0011 ,
ED
DSN
=6RTDR.SSPLIE.FORT,DISP=SHR
0012
'SO.
SYSIN PL

0013
4 0
404800
15
12
01
0 014
3 0
3 04:30 0
15
12
01
0015
50
5 04P 0 0
15
12
01
0 016 0 0 0 0 0 0 0 0 0 0000 00 0 0 0 00
0017
0018 FDJ
END OF li.lORK FILE
Fig. 1-2. Sample Input for Filter Program
246


256
variables) are expressed as a function of the past values
x^ and. x2 and' the: input E by
x* = (-Dx2+E)+C(x1+E)
x2 = Xl+E
y *2.
As the fourth order filter is implemented as a cascade, the
corresponding workspaces were overlapped one register to
pass automatically the output of the first resonator to the
second. The values of the filter coefficients, C and D,
were converted to hexadecimal as fractional numbers and
stored in the initialization. Generally they are less than
one, but C can be greater than unity, which means that if
the coefficients were stored preserving their relative mag
nitude, part of them will be only represented as 12 bits.
This is thought undesirable due to the quantization effects.
Therefore, it was decided to store all the coefficients
with full precision, leaving the alignment for the computa
tions. For instance, for one of the EEG filters the coef
ficients are
C1
= 1.3848
D = 0.7256
C2
are
= 0.5159
stored as
D2 = 0.7256
C,
= 1628
D, = B9C7
1
H
1 H
= 8417
n = B9C7 .
2
H
2 H


74
m.
a
2 _
e
-2b
2
12
and for rounding by
me =
(32)
(33)
The probability density function for the error process is
shown in Fig. 2. The autocovariance sequence of the error
is assumed to be
Yee(n) =Og6(n) (34)
for both rounding and truncation. The ratio of signal
power to noise power is a useful measure of the relative
strengths of the signal and the noise. For rounding or
truncation the signal to noise ratio is
(12.2
2b
(35)
or when expressed with a logarithmic scale
2
o 0
SNR = 10 log, f-|) = 6.02b+10.29-rlO log, rt(cT). (36)
10v 2J 10 e-


299
2114
390
MPY
1 ,7
2116
1503
JGT
P0ST7
2118
0A17
SLA
7.1
2 11A
0507
NEG
7
211C
1001
JMP
POSTS
211 E
0 417
P0ST7
SLA
7, 1
2120
A 1C9
POSTS
A
9,7
2122
C3C3
MOV
3, 1 5
2124
0 82F
L>
SR A
15.2
*
A
2ND
RESONATOR
2 126
02E0
LWPI
FORTH
212 8
FD3E
212A
0 743
A8S
3
212C
38C2
MPY
2, 3
2 12E
1101
JLT
POSTA
2130
0503
NEG
3
2132
AOCO
POSTA
A
0,3
2134
C243
MOV
3.9
2136
6 ICO
S
C 7
2138
C0C7
MOV
7,3
213A
C747
A3S
7
213C
390
MPY
1 ,7
2 13E
1503
JGT
POSTB
2140
OA 17
SLA
7,1
2 142
0507
NEG
7
2 144
1 001
JMP
POSTC
2 146
CA17
P0ST3
SLA
7, 1
2 143
A1C9
POST C
A
9, 7
2 1 4 A
0 43
MOV
3,5
2 14C
0335
SR A
5,3
2.14E
C805
MOV
5,aOUTl
2150
FD 66
2 152
0380
RTYJP
END
GAIN i:i.3
0* NO.OF ERRORS IN THIS ASSEMBLY^ 0000
OF RELOCATABLE LOCATIONS USED = 0000


270
1



309
TITL I NTHANF*
****3$:## *** ******* fr.#^**:*#*-**#:***:*
* INTHANDFREQ
***4 -***.*:*<: #**#*=(: 44 44 *444*4
* MODULE TO 3E USED WITH MA I NF
* BESIDES SETTING FS IT ALSO
* CALCULATES THE FREQ. AND ITS
4
RATE
OF CHANGE IN
A PRESCRI3ED
*
FREG,
BAND OF THE
INPUT
2200
AORG
>2200
FCOA
PERI C
EQU >FC0 A
FC08
DE TEC
EQU >FC08
FCOC
PWAV E
EQU >FC0C
2200
0201
LI
1, > 1EFO
2 20 2
1 EFO
2204
C 342
MOV
2,0>A< 1 )
2206
COOA
220 8
02 OC
LI
12.>100
220 A
C 1 00
220C
02 03
LI
3>187
220 E
0187
2210
33C3
LDCF
3,15
2212
IE 00
SDZ
0
2214
1 D03
S30
*3
221 6
C300
LI MI
3
2213
0 0 03
221 A
0 60 A
DEC
10
22 1C
1 603
JNE
TIME
2 21E
0569
INC
9
2220
0 2 0 A
LI
10,>F0
2222
0 OFO
2224
05CE
TIME
INCT
14
2226
06 20
DEC
3PERI0
MORE POINTS?
222S
FCOA
2 22 A
16 1C
JNE
CONT
2 22 C
C142
MOV
2,5
MIDDLE 3AND PEP IOD TO RS
2 22E
C320
MOV
SDETEC.3DETEC I NSAND WAVE?
223 0
FC08
223 2
FC08
2234
1306
JEQ
CONTI
2236
C820
MOV
223 8
FCOC
223 A
FCOA
223C
04E0
CLP.
SDET EC
CLEAR FLAG
223E
FC OS
2 24 0
1004
JMP
C0NT2
2242
C802
CONTI
MOV
2.DPER 10
PERIOD GETS MIDDLE VALUE
2244
FC OA
2 246
C444
MOV
4, *1
OUTPUT
2248
10 0D
JMP
CONT
224A
6 160
CO NT 2
S
SPERIC,5
GET PERIOD DIFF
224 C
FCOA
224E
0 A 1 5
SLA
5,1
AMP. IT
2250
C4 45
MOV
5,41
2252
61 85
S
5,6
SUBT. FRO* PREVIOUS
2254
0746
A3S
6
2 256
39A0
MPY
2PERI0,6
GET RATE GF CHANGE
2258
FCOA
2 2SA
1501
JGT
POST
225C
0507
NEG
7
225E
Cl 85
POST
MOV
5,6
UPDATE OLO PERIOD
2260
C 307
MOV
7 ,3> 1EF2
OUTPUT RATE GF CHANGE
2262
1 EF2
2264
0380
CONT
RTWP
END


281


318


235
the development of a portable seizure detector, using the
proposed design. Studies are under way toward this direc
tion.
The constancy of the period parameters in the PM
paroxysms is intriguing, when seen from the variability of
the EEG normal rhythms. Also the abrupt beginning and end
of the paroxysm are intriguing. Is there any seizure
parameter which can be coupled with the end of seizure?
Again one of the candidates is the PM recruiting rate,
since it is known that it slows down generally towards the
end of seizure. A slight modification in the PM detector
is being evaluated at this time to study the frequency
variation in narrow EEG frequency bands (programs MAINF
and INTHANF). The system's output is a pulse, modulated in
amplitude with the period of the waves, which meets the
period criteria. Figs. 51a and b show examples of the out
put (channel III) for two different seizures. The rate of
change of frequency is also outputted (channel IV).
Another area which will be interesting to study is the
relation of background activity and seizure occurrence.
The EEG laboratory at the University of Florida is now
capable of performing such automated analysis using the
described PM detector and the Sleep Analyzing Hybrid Com
puter (Smith, 1978), which is really an EEG waveform ana
lyzer. Correlations between the presence of seizures and
predominant EEG backgrounds can be investigated.


277
2 40E
CO 02
MOV
2,0
2410
4020
SZC
DMASK,0
241 2
FC06
24 14
0280
Cl
C,>0000
2416
00 00
241 a
1 3 04
JEQ
POST
24 1 A
a 0C2
C
2,3
241 C
13EF
JEQ
CUME
241 E
15EE
JGT
CUME
2420
1 ODF
JMP
NEG
2422
0589
POST
INC
9
2424
8 0C2
C
2 ,3
2426
13EA
JEQ
CUME
2428
1 5E9
JGT
CUME
242A
0284
Cl
4,TPLUS
242 C
00 3C
2 42E
15BA
JGT
PEAK
2430
0284
Cl
4,TMINU
2432
00 14
2434
116 7
JLT
PEAK
2436
60CC
5
12 ,3
2438
8 8 03
y**
V.
3 cDTHRES
243 A
PC 04
2 43C
1 1 B3
JLT
PEAK
243E
CS03
MOV
3,3WSTA4
2 44 0
FE 00
2442
0420
3LWP
SSTAT4
2444
FC1A
$
*
3RD LC
UP
2446
C0C2
POST 2
MO V
2,3
2448
0581
INC
1
2 4 4 A
0589
INC
9
2 44 C
0407
3LWP
7
2 44 E
C802
MOV
2,3>IEF0
2450
1EF 0
2452
0405
3LWP
5
2454
CO 02
MOV
2.0
2456
4020
SZC
2MASK,0
2458
FC06
245A
0280
Cl
0,0000
2 45 C
0000
2456
1 3F3
JEG
POST2
246 C
C 8 04
MO V
4 S> WSTA2
2462
FDCO
2464
0420
3LWP
3STAT2
2466
FC 12
246 8
0289
Cl
9,TPLUS
246A
003C
2 46C
1598
JGT
PEAK
2 46 5
0289
C I
9, TM INU
2470
00 14
2472
1 198
JLT
PEAK
2 47 4
0204
LI
4, >800
2476
0300
2478
C 3 04
MOV
4 5 IEF2
247 A
IEF2
2 47C
04 58
3
*1 1
END
DATA POSIT?
INCREASING?
NCT MONOTONIC.GO TO NEG
ZERO CROSSING REACHED
PEAK?
VAL-PEAK WITHIN LIMITS
RESTART SEARCH
GET PEAK-VAL AMP
> 75 UV?
RESTART SEARCH
P ASS PEAK TO ST AT I S
POS TO NEG ZERO CROS?
PASS VAL-PEAK TIME TC
WITHIN LIMITS?
NO RESTART SEARCH
S.W. RECOGNIZED
OUTPUT NEG PULSE
GO TO MAIM
NO.OF ERRORS IN THIS ASSEMBLY^ 0000
RELOCATABLE LOCATIONS USED = 0000
STAT IS


13
used ARMA models to extract alpha, beta, delta, and theta
band intensities for automatic EEG classifications.
Mathieu (1970, 1976) used AR models in sleep scoring.
Jones (1974) compared the window lag estimation with AR
estimator to determine power spectral and coherence func
tions in the neonate EEGs. Gersch and Yonemoto (1977) com
pared the AR and ARMA models for the power spectrum estima
tion of EEG. The same authors (1973) also used parametric
AR models to apply the Shannon-Gelfand-Yaglom amount of
information measure in sleep scoring.
In epilepsy AR models have been used toanalyze the
ictal event. Gersch and Goddard (1970) used the partial
coherence among time series to extract information about
driving. Tharp (1972) and Tharp and Gersch (1975) use a
similar procedure to determine seizure focus. Herolf
(1973) and Lopes da Silva et al. (1975) also use an AR model
to perform seizure detections by inverse filtering.
Another concern faced in spectral analysis is the
presentation of the results. Due to the specific tech
niques involved, the results need to be further processed
to be readily interpreted by the neurologist. The main
goals are data reduction and readability. The compressed
spectral array of Bickford et al. (1973) has been exten
sively used and summarizes pretty well the changes of EEG
with some external factors (different behavioral states,
tracking of alpha waves with light stimuli, hemispheric
symmetry, acute slow wave abnormalities). The canonogram


54
it is possible to design bandpass filters using the direct
substitution to map the filter poles and a technique
derived from the bilinear to map the filter zeros. The
relations between the design and the implementation are
apparent in the choice of integer zeros (to cut computa
tion time and roundoff noise) and in the choice of the
transformation, which may help controlling the midband
filter magnification.
Finite Length Effects of the Implementation
After obtaining the filter transfer function in the
Z domain, the filter algorithm is the inverse Z transform
of H(z). For a second order function of the special type
which will be used here, H(z) can be written as in (15) and
y(nT) as in (16).
H (z)
(z+1)
(z2-Cz+D)
(15)
yn = Cyn-l-Dyn-2+xn-xn-l
(16)
The filtering will then be accomplished by computing (16)
in the microcomputer.
If an infinite wordlength machine is assumed, the
implementation problem is nonexistent. Practically finite
wordlengths must be used leading to the fact that almost
every digital filter is nonlinear. For this reason the
output of the digital filter deviates from what is actually
desired. This leads to the study of various ways of


166
F3-A1, F4-A2, C3-A1, C4-A2. Besides the paper record
obtained on a Grass Model 6, the sessions were tape
recorded on an FM tape recorder Sanborn Model 3900, at
1 7/8"/sec. In the beginning and at the end of each ses
sion a 50 yV, 10 Hz sinusoidal calibration signal was
recorded on each tape (50").
Two types of logging were utilized: a ten-minute log
describing the activities of the patient (awake, sleeping,
walking, eating) and a tape log giving important information
about tape number, beginning footage, recording conditions,
EEG montage used, etc. Fig. 30 presents a copy of the
technical log utilized.
The specifications of the telemetry system, regarding
signal fidelity, were judged appropriate (40 dB S/N ratio,
0.5-100 Hz frequency response) although some clipping
occurred (200 yV maximum signal). The tape recorder band
width at 1 7/8" was 0-256 Hz, with a signal to noise ratio
of 35 dB.
Some technical problems arose, mainly with the teleme
try unit. Also some of the tapes did not have a proper
calibration (very noisy signal), or the technician changed
gains in the middle of the session to avoid clipping of the
EEG. However, it is estimated that 90 percent of the 110
tapes have good quality data. One aspect that deserves
mentioning is the lack of a time code recorded on the
tapes. For synchronization purposes its information would
be very convenient.


234
to help set dose levels of anticonvulsant medication. For
instance, the patient is given a certain drug dosage, and
the EEG is analyzed for the next day to assess the reduc
tion in seizures.
The generation of statistics for the detection param
eters can be utilized to further quantify the PM patterns
in the EEG. Up to now relations between drug administra
tion and changes in the PM patterns have not been addressed.
For research purposes, to assess how the drug is actuating
and ultimately to understand better the PM generation, this
aspect is important. Moreover, it may turn out that cer
tain parameters (the repetition rate of the wave complexes
is a good candidate) will be sensitive indicators of drug
levels and could therefore be used to prescribe the dos
ages.
The above study requires new sets of data because it
will be of paramount importance to quantify adequately the
occurrence of the PM in humans before any anticonvulsant
medication is administered.
It will be important, for instance, to study the
ultradian characteristics of PM activity. The correlation
of seizure duration-interictal intervals with physiological
states seems very interesting as the preliminary results of
Stevens et al. (1971) and the observations on patient #4
show. The present system output can be used for this pur
pose without modifications. To accomplish this study a
24-hour patient monitoring is desirable, which points to


326


22E8
04 C 3
CLR
8
2 SEA
0588
LOOP
INC
a
22EC
C12A
MOV
3>A( 10 ) 4
DEL X IN 4
22EE
COOA
22FC
3908
MPY
8,4
N* QELX/DELY IN R4
22F2
3D2 A
DI V
3>C( 10 ) 4
22F4
OOOC
22F
C16A
MOV
321 10),5
OLD X IN R5
2 2F a
0002
2 2FA
4 1E A
SZC
3>£{ 10 ) ,7
DEL Y +?
22FC
QCOE
2 2FE
13 03
JEQ
POS
23C 0
062A
DEC
14(10)
NO, DEC OLDY
2302
0004
2304
10 02
JMP
COMI
2306
0 5AA
POS
INC
24{10)
2308
00 04
22 QA
4 1 AA
com
SZC
3>E(10) .6
DEL X +?
230 C
00 OE
230E
1601
JNE
POS 1
221 0
0504
NEG
4
2312
A 144
FOSl
A
4,5
ADO DEL X TO X
2314
CA6A
MOV
24(10),32(9)
OUTPUT NEX X Y
22 1 6
0004
2313
0002
231 4
C 645
MOV
5, *9
221 C
0 69C
GL
*12
231 E
8A AA
C
34( 10),33( 10 )
F INISHED?
2220
GO 04
2222
0 0 08
2324
16E2
JNE
LOOP
222 6
CAAA
MOV
36(10),32(10)
UPDATE NEW X (ROUNDING)
2223
0006
2 32 A
0002
222C
0380
RTViP
*
SAME
THING BUT DEL Y/DEL X
222 E
C4C3
YS IG
CLR
8
2330
0538
LCP
INC
8
2232
C12A
MOV
2>C( 10) ,4
2334
cooc
2336
3 908
MPY
8,4
2333
3D2A
DI V
3>A( 10 ) .4
233 A
00 0A
233C
Cl 6A
MGV
24(10),5
233E
0 0 04
2 340
41 AA
SZC
3>E( 10).
2242
00 CE
2344
16 03
JNE
PO 32
2346
062 A
DEC
22{10)
2343
0 0 02
234 A
1002
JMP
CON 3
234C
05 AA
P0S2
INC
32(10)


TABLE VIIcontinued
PATIENT #12
*Just one Sz > 3 sec
195


217


29
computation wordlength to obtain a certain output signal
to noise ratio.
In Chapter III the model for the petit mal activity
utilized in the detection will be presented, along with its
implementation on a microcomputer. The system's testing
will also be explained there.
As this research work is primarily engineering
oriented (a new instrumentation system is designed around a
new model of the petit mal activity), the system's evalua
tion is presented in Chapter IV. Preliminary data demon
strating the high resolution capabilities of the detector
and its use in quantifying the petit mal seizure data will
also be presented.


62
must be scaled so that the output, yn are a number of approaches that can be considered to accom
plish this (Oppenheim & .Shafer, 1975).
As
00
88 I hk*n-k <24>
k=0
where h^ is the filter response, it is easy to see that
IyJ l IhkNxn-kI (max|xk|) £ |hk|. (25)
k=0 k=0
00
Therefore, by making max|xv| = 1/ £ |h, |, overflow of y can
K k=0 K n
be prevented. This means on the other hand that the zero
forming paths of the filter must be multiplied by
CO
k = 1/ £ |h |. Experiments have shown that this scaling
k=0 k
policy is too pessimistic and does not allow good use of
the full dynamic range of the wordlength.
A second approach would be to assume the input sinus
oidal, with a frequency equal to the resonant frequency(es)
of the filter. This is equivalent to requiring (H( ) is
the filter's frequency response)
|H(e^X) | < 1 -TT < X < ir (26)
and is accomplished by multiplying the coefficients by k,
the scaling constant, so that


285


248
132
131
21
133
13
aa
a
C
42
2*
110
70
1 5
16
7
17
13
C
C
C
60
61
62
6
63
C
140
141
00 132 1st,MN
X1*2*1*1
hB8*wB/W0
u-2*Psecn*PT:irn*wBB**2
a 31 -wbh *? r cps crn **a-(piM cm **2)
AAsSQPTC (SGPTCA**2+B**21i-A1/2.1
8R3QPT( C3QiT(A**?+fl**2)-A) / 2.5
xi2*r
PPECII3 aWP*CWP5*PPECIT)-9P)
PT^Cin*tiO*<--6B*PICTI)*AA)
GO TQ 133..
00 21 1*1. N ,
PfiCI3apREri)*Ja
PIHfT3ariO*PInCT3*WP
oo 134 rt.N
PSCI3CMP|.XfPPEf II /PIKCT) )
P7(n*cExPP8nr
cofJTr'ue
wPI7£fj,aai
FOUH AT 11H11
SITE(6r<0 CPSCI1.
FnWMATClHn50X,7HP33,2F17.71
cnNTijunus xanO Pi33 FILTER
TOa*O.Q
nM*N
00 43 >1*1,100
TC*0>1PI_XC1 .0,0.0)
WC9£M)CU0-WCU1Wfl.-FLOAT(M-l)*0.02)*2.+0
MCbHaCHPLXCO.OjWCPCm
00 42 J*1,N.
rc*Tc*CWCPHnP3(J) WxCSH-CONJGCPSC Jl) 1
IF CNWIO.EG.Ol MNaN+1
WCDfa)*TC/wra(hl**(Nn-11
AC*CaP3 fWC8CM)**(MM 11/TO 1
IFCiC-T0ai4T,3,4t
TOQtaC
CONTINUE
WRITE (6, M3) TOO
FQPmATCIUQ.16H GAIN OF FILTER* r F16,4 3
00 70 H* i ,100
TKP in) ai r AM (A T.liC CWCO CM) ) /REAL (wco m 1 3
TXo (Ml SCABS f 1 ./ creu*wco con 3
^3,1=1,11
wRITE C, 163
FOUMATItHO)
FOHH!rUoY.?WPLQ'r OF SAMO PASS FILTER)
call plotcwra*tkb.tool
00 .7 1*1.10
ipitec, m
FOHKATC1HO)
EVAI UiTIOM nF IMS mAGmITUOE A NO PHASE p THF OIGITaL FUTES USING
OIHECT mapping of PnLFS A'JQ SEARCHING SYMMETRY ACROSS THE BANG
CASCADE S F AI IZATION .
Ka(l .+C03 r40*f31 / f 1 .-COS C'40*T3 3
IFCK+1-M16G,61,62
ko*n-k*i
M 3K
<0*0
Kt*K
<0*0
X!N-1
<2*1
IE CNWIO.Ea.33 X2*2
FOHHa^^i isHNiiMBEP OF ZEROS at THE CRIGTn AMO Z*-1)
WPITE Co,6*1XQ,K1
F0WMaT(IHO.30X,3HX0s, 2.30X, 3HKla, l'i)
GO TO 147
HTGH PASS toamsfophattcn
00 141 t 1,M .
PS(IIS40U/P3(13
PZ(i5*cexP{PsCi)*T)
TCC-0,0
00 142 1*1.100
rr*CMPLX(i.0*0.0)




279
Yes


254
j^INTHANDLER ^
/
/
/
/
/
/
/
/
V
t
Initiate A/D

>
>
Set sampling
frequency
\
>
^ Return ^
Fig. II-2. Flow Chart of Filter


291


microcomputer and a 12 bit A/D converter were utilized.
With the procedure, a fourth order bandpass filtering func
tion can be accomplished in less than 300 ys.
Time domain parameters were selected to arrive at a PM
seizure model which would be applicable to the detection of
classical PM and PM variant epilepsies. The parameters
were translated into electronic quantities and implemented
in a microcomputer.
For the first time in the automated analysis of EEG,
a microcomputer based system was built for the processing
of one channel of data, using a completely digital, real
time, detection scheme. All the programs which comprise
the detector were written in assembly language, and care
was taken to reduce the interactions between program
modules. The top-down program approach was utilized.
The system was tested and evaluated with data from
epileptics collected in the Veterans Administration Hospi
tal, Neurology Service, from an ongoing drug study. A
telemetry link was used to record the EEG, allowing the
patient to move at will in a 3 x 5 meters room. Six
patients who showed the largest number of seizures were
selected for the evaluation. A total of 70 hours of data
was analyzed.
The agreement in the detections with the human scorer,
for seizures (Sz) greater than three seconds, was 86 per
cent. If the sorting of seizures in the groups 3 < Sz
vii


342
Rabiner, L., and B. Gold. Theory and Applications of
Digital Signal Processing. Prentice-Hall, Englewood
Cliffs, New Jersey, 1975.
Remond, A., and B. Renault. "La Theory des Objects Elec-
trographique." R. Rev. EEG Neurophysiol., 2:241-256,
1972.
Remond, A. "Reviews in Epilepsy." Hndbook of Electroen
cephalography and Clinical Neurophysiol., 13a, 1974.
Robinson, E. A. Statistical Communication and Detection.
Hafner, New York, 1967.
Rosadini, G., Cavazza, B., and F. Ferrillo. "On the Organ
ization of Electroencephalographic Rhythms in the
Sleeping Man." Acta Neurol. Lat. Amer., pp. 200-217,
1968.
Rose, S. W. "Reliability and Validity of Visual EEG Assess
ment in Third-Grade Children." Clin. EEG, 4:197-205,
1973.
Saltzberg, B. "Detection of Focal Depth Spiking in the
Scalp of EEG Monkeys." Electroenceph. Clin. Neuro-
physiol^, 31:327-333, 1971.
Saltzberg, B. "Theoretical and Experimental Investigation
of the EEG Signals Using Parameter Tracking and
Matched Filtering." Doctoral Dissertation, Marquette
Univ., Milwaukee, 1972.
Sandberg, I. W., and J. F. Kaiser. "A Bound on Limit
Cycles in Fixed Point Implementation of Digital Fil
ters." IEEE Trans. Audio Electroacoust., AU-20:110-
112, 1972.
Schenk, G. K. "The Quantification of EEG by Vectoral Iter
ation Techniques: A Simulation Method of Visual EEG
Analysis." Electroenceph. Clin. Neurophysiol., 37:106,
1974.
Schenk, G. K. "The Pattern Oriented Aspect of EEG Quanti
fication." In Quantitative Studies in Epilepsy.
Raven Press, New York, pp. 431-462, 1976.
Schmidt, R. P., and B. J. Wilder. Epilepsy. Davis, Phila
delphia, 1968.
Sellden, U. "Psychotechnical Performance Related to Parox
ismal Discharges in the EEG." Clin. Electroenceph.,
2:18-27, 1971.


175
(computer versus human) were built for each patient. They
included the sorting of seizures (Sz) in three categories
(l10 sec) according to the neurologists.
The computer agreement with the detection of seizure (first
line), the computer agreement with the sorting (second
line), and the total time in agreement (third line) are
also presented. The first information answers the question,
"did the computer recognize this seizure?" More important,
however, is the second parameter, which is related to the
aspect of sorting, since it has a higher physiological
significance.
To assess the reliability of the computer performance
as the "leading" output, not only the agreement with human
is important but also the false detections. The picture of
computer performance is acquired from the three last lines
of the tables. Table IV presents the totals for each
patient analyzed. The purpose is to analyze any dependence
of performance with the pattern (e.g., PM classical versus
PM variant). The computer performs well with respect to
sorting in the classical PM patterns as expected, since the
key aspect of these is regularity. Take, for instance, #7,
where the agreement is 100 percent in Sz>10 sec, and #12,
where the agreement is very good for 3 scored two Sz>10, but their duration was 10.4 secsee
total time). Patient #5 also had an excellent agreement in
the two first sessions, but in the third (after Depakene
administration) there was a greater variability in the PM


156
rate were recognized), up to the last slow wave before the
positive going pulse is outputted. This pulse means that
no slow waves were recognized in the last second or that
the period does not meet the requirements twice, consecu
tively.
The statistics are stored in memory beginning in RAM
address 2720. The format of the seizure data is the fol-
ri
lowing, for seizure > 3 sec:
FFFF (SEPARATION TAG)
Time of occurrence (sec)
Duration (# of points)
(X) repetition period (# of points)
(a ) variance of repetition period (# of points)
(X) 1/2 period of waves (# of points)
(a ) variance of 1/2 period of waves (# of points)
(X) delay spike/S.W. (# of points)
2
(a ) variance of delay spike/S.W. (# of points)
(X) amplitude of filtered S.W. (level of A/D conversion)
2
(a ) variance of amplitude of filtered S.W. (level of A/D
conversion)
(X) amplitude of filtered spike (level of A/D conversion)
2
(a ) variance of amplitude of filtered spike (level of A/D
conversion)
FFFF (SEPARATION TAG)
For seizure less than 3 sec only the two first parameters
are stored. The system output also includes the number of
seizures (Sz) detected in each of the categories Sz<3 sec,


.945 sec
o
0.062 sec
Fig. 44b. Variance Repetition Period Versus Repetition Period (#5-2)
220


49
Another conclusion of the analysis which is very
important regards the filter passband gain. In digital
filter design the control of the filter midband gain is
generally accomplished by properly scaling the filter
transfer function. It is suggested that the correct
handling of the Z plane filter design may constitute an
alternate way to control the midband gain, at least in some
cases. An example given in (Principe et al., 1979) is
worth mentioning. For the delta filter (0.1-3 Hz,
fs=100 Hz), the midband gain was decreased from 878 for the
filter designed with the narrowband direct substitution to
87 just by using the wideband transformation (both fre
quency responses met the specifications).
Let us analyze in general the effect of the zeros at
z=l in the transfer function. For the zero at z=l the
numerator takes the form
(10)
and for the zero at z=-l
|z+1| = 4 cos2
(11)
It is concluded that the effect of the zero at z=-l has the
symmetric effect of the zero at z=l, with respect to fs/2,
so whatever conclusion is reached for one will apply for
the other in the symmetric region. Fig. la shows the
attenuation characteristics of EQ(10),(11). Now suppose


5
fact, the procedure displays more points of the discrete
Fourier transform (DFT), and so a better approximation to
the Z transform is achieved. However, the Z transform
remains the same (as long as the record length is con
stant) so the initial resolution is kept unchanged.
Another problem encountered is the estimation of the
power spectrum. Let us resume the estimation process. To
compute the essential statistical properties of a Gaussian
random process the more general way is to evaluate the
autocorrelation function by ensemble average. The method
is computationally expensive since various sample sequences
of the process have to be available. If the random process
is ergodic (Lee, 1960; Thomas, 1969), then it is correct to
compute the autocorrelation function by a time average only
over one sequence. There are fewer memory requirements
involved, but as the properties of the random process are
to be inferred from the ones calculated in the sample
sequence, consistent estimators have to be used (i.e.,
estimators that are unbiased and whose variance decreases
with the number of data points). It is very easy to find
consistent estimators for the autocorrelation functions
(Oppenheim and .Shafer:,. 1975). The problem arises when the
goal is to estimate the power spectrum. It is not true in
general that the Fourier transform of a consistent esti
mator of the autocorrelation function (periodogram) will
produce a good estimate of the power spectrum (Barlett,
1953; Jenkins & Watts, 1969). When an infinite number of


183
the seizure count due to desynchronization, still detecting
slow waves with the right repetition rate, but not calling
the event a new seizure due to the absence of spikes.
Fig. 32 exemplifies the explanation. Probably more impor
tant than the discrepancy in seizure duration is the
appearance of a large number of misses in this group of
patients (16.7 percent). They occurred mainly in patient
#3 and were due to the nonexistence of well-defined spikes.
This fact probably calls for a modification in the detec
tion algorithm.
Table V presents the final agreement averaged over the
six patients studied. The discussion will be directed
towards the clinical significant seizures, i.e., seizure >
3 sec. The agreement of the computer versus the human with
respect to seizure detection is 100 percent for seizure >
10 sec and 88 percent for 3 < Sz < 10 sec. The agreement
for Sz > 3 sec is 91 percent. If the sorting of the sei
zures in the categories is taken into consideration, the
agreement drops to 86, 73 and 77 percent, respectively.
The total time in agreement is 83, 94 and 89 percent,
respectively, for 3 < Sz < 10, Sz > 10, Sz > 3 sec. How
ever, as these numbers are totals, positive and negative
errors can compensate each other. Therefore, some caution
shall be exercised in their interpretation.
The computer counts are also presented in Table V.
They are intended to judge the system usefulness as the
only scorer, now that the agreement with the human has been


128
energy (spikes), the output of the filter will tend to
display the effect of the impulse response decay, shifting
negatively the zero (d.c.) level. To detect the slow waves
in the four subjects, the half period requirements were set
at
High period ... 0.083 sec (14)
11
Low period ... 0.200 sec (30H)
which corresponds to frequencies of 6 to 2.5 Hz. Further
in the testing it was found that this measure (peak-to-
valley) alone is very sensitive to artifacts since the
response of the slow wave bandpass filter to a step input
mimics exactly the period window. Assuming that the band
pass filter preserves the lowpass characteristics, but
introduces a time scale warp (Blinchikoff, 1976), the rise
time was found to be 0.14 sec. Therefore, a maximum period
of 0.5 sec (3C) between the zero crossings was also
£1
required (points B and D).
Periodicity of the PM Complexes
If the filters were good enough to attenuate the spike
component, only this measure would be necessary to detect
the PM slow wave component. However, only higher Q, or
higher order filters would be necessary, giving heavier
weight to the undesirable ringing phenomena.
The period of the slow wave component was measured
between peaks, since these points are detected in the pre
vious measure. The periodicity window was set between


16
prediction scheme. He implements the inverse filter of the
all-pole approximation model of the EEG and monitors the
error between the predicted value and the real data points.
Deviations above a prescribed threshold are correlated with
nbnstationarities of the input EEG data. Very similar
techniques are used in EEG adaptative segmentation proce
dures (Bodestein & Praetorious, 1977) which could eventual
ly lead to transient event detection. A combination of the
nonstationary information of the phasic events and the
sharpness of the spikes was combined by Birkemeier et al.
(1978) to increase the resolution separation of the clusters
of epileptic transients and background activity. The
system requires settings for each patient and works better
in epochs with few spikes (otherwise they may bias the
estimation). It is sensitive to artifacts.
Etevenon et al. (1976) use null-phase inverse filter
ing to deconvolve the EEG and then detect fast activity.
His method is equivalent to the one just described (Lopes
da Silva), but it is executed in the frequency domain.
From the EEG sequence the power spectrum is calculated
through the periodogram, and after smoothing and whitening
the amplitude spectrum is obtained by evaluating the square
root. Then the inverse of the spectrum is computed, multi
plied by the Fourier transform of the incoming EEG, and the
inverse FFT taken. This signal accentuates sharp tran
sients contained in the EEG, and after threshold detection
they can be extracted.


136
ia = w-* sin w(tw-At) = w-* sin wt.
max
cos wAt
+ A cos wt,
max
sin wAt = \axU"cos wAt)
(54)
and
At = l/2fs.
For
fs = 240 Hz and w = 2ttx10
AA
(1-0.9914)
i.e., the error is better than 0.9 percent. The repeata
bility is also good, because an average over 64 cycles is
performed. Fig. 21 shows a typical output.
System Implementation
The PM seizure detector was implemented around a
TMS 9900 16 bit microprocessor. The system's block diagram
is shown in Fig. 22, and it incorporated the TMS 990/101-M
microcomputer board, TMS 201/2 memory expansion board and
the Analog Devices RTI 1240 I/O board. The I/O board,
which plugs directly in the TI bus in a memory mapped con
figuration, is a 16 channel multiplexed, 12 bit D/A and two,
12 bit D/A.channels. The memory mapping of the TI micro
computer as used is shown in Fig. 23.


135
beginning a program module looked at the peaks of the
calibration sinewave and computed the average over 64
peaks. The number obtained corresponds to 25 yV (the
calibration sine is 50 yV p.p.). Then, knowing the mid
band gain for each of the filters and the desired threshold
level, the amplitude at the filter output that corresponds
to 75 yV can be immediately obtained by a multiplication
(75/25 x gain). This new number was stored in a memory
location used in the program as the threshold. The cali
bration was then performed without operator's interven
tion, reducing one important step of possible errors. The
precision in the determination of the peak was very good,
since the sampling frequency is 240 Hz and the calibration
sine is 10 Hz. The maximum errors can be computed by the
following derivation (complemented by Fig. 20):
Fig. 20


45 sec
t
202


224C
2 24 E
2250
2252
2254
2256
2253
225 A
225C
225E
226 0
2262
2264
2266
2263
2 26 A
226C
226 E
2 27 0
2272
2274
2 27 6
2278
2 27 A
2 27C
227 E
2230
2282
2234
223 6
2233
229 A
2 28C
228 E
2 29 0
2292
229 4
2296
2 29 8
229 A
2 29C
2 2 9 E
22A0
2 2A2
22A4
22A6
2 2A8
2 2AA
22AC
22AE
22 EG
22B2
2284
2 236
04E0
CLR
3FLAG
NO TOT
FC22
0201
LI
1 ,PC1
ADDR 0
FCOS
02 02
LI
2 >24A 8
JUMP
24A8
CC42
MOV
2 *1 +
0202
LI
2 >24C0
2ND
24C0
CC42
MOV
2 l +
0202
LI
2 >2400
3RD
2 4D0
CC42
MOV
2, *1 +
02 02
LI
2 >FD AO
WS P
F DAO
CC42
MOV
2 *1 +
0202
LI
2 ,>2590
PC
2590
CC42
MCV
2 ,*1 +
0202
LI
2 >FDC0
WSP
FOCO
CC42
MOV
2**1 +
CC61
MCV
3-4( l ) ,* 1 +
1
FFFC
0202
LI
2 >FDE0
WSP
FDEC
CC42
MOV
2**1 +
CC 61
MOV
2>-4( I ) .*1 +
FFFC
0202
LI
2 *>FE0
WS 1
OFEC
CC42
MCV
2**1 +
CC 61
MOV
3-4 FFFC
0202
LI
2 >FE20
wsp
FE 20
CC42
MOV
2, *1 +
CC61
MOV
a-4(i), i +
!
FFFC
0202
LI
2,> OFFF
MASK !
OFFF
C802
MOV
2.3MASK4
FC26
02 02
LI
2 >OQFF
MASK !
OOFF
C802
MOV
2,3 M AS K 8
FC 23
0205
LI
5,>7FFF
MA SK
7FFF
C 3 05
MOV
5 3MA SK
FC06
0300
LI MI
3 I NT R
MASK '
0003
02 05
LI
5,WPIKE
WSP
2ND JUMP TO SPIKE
RD JUMP TO SPIKE
SP FCR ST AT IS 1
PC FCR ST AT IS 1
WSP FOR STATS 2
PC FOR STATS 2
FOR STATS 3
PC FOR STATS 3
FOR STATS 40
PC FOR STATS 4
FOR STATS 5
PC FOR STATS 5
MASK FOR CONVERSION


238
As a concluding remark it is appropriate to praise the
use of microcomputers for the versatility given to the
detection scheme. The great number of changes in the cri
teria performed during the detector design were easily
accomplished by correcting programs, not cutting wires.
With adequate software developing facilities the design
time can be shortened, but better yet, it enables updating
or modification of features in a final product. For
instance, suppose that the criteria of detection are judged
too loose for a specific application (e.g., study only
classical PM patients), a simple modification in one of the
program modules will change the criteria from three slow
waves and at least one spike to spike/slow wave three
times, decreasing appreciably the false alarm rate.
Another example is to customize the PM parameters for the
pattern of a certain patient.
The power of the pattern recognition algorithm and the
on line statistics generation also attest the advantages of
the use of microcomputers.
It is our belief that the system presented in this
dissertation, as well as its future developments, will
become a valuable tool in PM epilepsy research and also in
medical diagnosis and health care.


90
filters with only 4 multiplications per cycle, allowing
sampling frequencies up to 3 KHZ.
Signal to Noise Ratio Specification
Now that the output noise can be calculated and the
filter magnification is known, the important step of choos
ing the hardware to obtain a given output signal to noise
ratio can be addressed. From the specification involving
the output signal to noise ratio and the degradation pro
duced in the filtering, the input signal to noise ratio can
be calculated, which sets the input wordlength. If the
analog dynamic range is smaller, an A/D converter that
spans the analog dynamic range shall be chosen and a shift
left operation up to the requirement of the input word-
length shall be performed. From the internal magnification
analysis the increase in wordlength can be determined and
added to the input wordlength to set the computation number
of bits.
In the present form a 12 bit A/D converter and a 16
bit microcomputer are being utilized, allowing for the
implementation of filters with gain of 16 or less. There
may be cases where a longer computation register length may
be desirable, but on the other hand a 12 bit A/D converter
may be excessive for EEG processing, mainly when the data
are prerecorded on analog tape. The dynamic range of a
Sangamo 3500 is 46 dB at 60"/sec. (manufacturer specifica
tions) which suggests that an 8 bit A/D is sufficient.


332
234E
0002
2350
4 1 EA
C0N3
SZC
£>E( 10) 7
2352
OOOE
235 4
1301
JEQ
P0S3
2356
0504
NEG
4
2358
A144
P0S3
A
4,5
235A
C66A
MOV
32(10) ,*9
235 C
0002
235E
CA45
MOV
5,32(9)
2360
0002
2362
069C
BL
*12
2364
SAAA
C
£2(10) ,£6(10 )
2366
0002
2368
00 06
236A
1 6E2
JNO
LOP
236C
CAAA
MOV
23(10),£4(10)
23E
0008
2370
0004
2372
0380
RTWP
2374
41 AA
FLAT
SZC
£>E (10,6
CHECK SIGN OF DEL X
2376
OOOE
2378
1 6C3
JNE
PCS4
237A
0 62 A
DEC
32(10)
237C
0002
237E
1002
JMP
COM4
2330
05AA
PC S4
INC
£2<10)
2382
0002
2384
C66A
C0N4
MOV
£2(10),*9
OUTPUT X,Y
238 6
0002
2333
CA6A
MOV
34{10),£2(9)
233A
C 004
23SC
0002
238E
G69C
3L
*12
2330
8AAA
C
22( 10) ,£6( 10)
2 392
0002
2394
00 06
2336
1 1 EE
JLT
FLAT
239 3
0380
RTWP
*
INTE
NSIFY CCRU BIT 26)
239A
CA 8C

MOV
12,£>16i10 >
SAVE VALUE CF R12
239 C
00 16
239E
020C
LI
12,>120
2 3A0
0120
23A2
1 D08
S30
8
OUTPUT *5 V TO CRU
2 2A4
C53C
WIDTH
INC
12
FORM 4 PULSE
2 3A6
028C
Cl
12,>140
23A8
0140
22AA
l 1FC
JLT
WIDTH
23AC
020C
LI
12,>120
23AE
0120
2330
1 E08
SSZ
a
OUTPUT ZERO TO CRU
23B2
C32A
MOV
2>16(10),12
233 4
0016
2 336
Q4oB
E
*11
END
)* NO.OF ERRORS IN THIS ASSEMBLY* 0000
JF RELOCATABLE LOCATIONS USEC = 0000


337
Gersch, W. "Spectral Analysis of EEG by Autoregressive
Decomposition of Time Series." Math. Bioscience,
7:205-222, 1970.
Gersch, W., and D. R. Sharpe. "Estimation of Power Spectra
with Finite Order Autoregressive Models." IEEE Trans.
Automatic Control, AC-18:367-369, 1973.
Gersch, W., and J. Yonemoto. "Parametric Time Series
Models for Multivariate EEG Analysis." Computers and
Biomedical Research, 10:113-125, 1973.
Gersch, W., and J. Yonemoto. "Automatic Classification of
Multivariate EEG Using an Amount of Information Meas
ure and Eigenvalues of Parametric Time Series." Com
puters in Biomedical Research, 10:297-318, 1977.
Gersch, W., and G. Goddard. "Locating the Site of Epilep
tic Focus by Spectral Analysis." Science, 169:701-
702, 1970.
Gevins, A. S., and E. L. Yeager. "EEG Spectral Analysis in
Real Time." In DECUS Spring Proceedings, pp. 71-80,
1972.
Gevins, A. S., Yeager, C. L., Diamond, S. L., Spire, J. P.,
Zeitlin, G. M., and A. H. Gevins. "Automated Analysis
of the Electrical Activity of the Human Brain: A
Progress Report." Proceedings IEEE, 63:1382-1399,
1975.
Gevins, A. S., Yeager, C. L., Diamond, S. L., Zeitlin,
G. M., Spire, J. P., and A. H. Gevins. "Sharp Tran
sient Analysis and Threshold Linear Coherence Spectra
of Paroxisms." EEG in Quantitative Studies in Epilep
sy. Raven Press, New York, pp. 463-482, 1976.
Giannitrapani, D., and L. Kayton. "Schizophrenia and EEG
Spectral Analysis." EEG Clinical Neurophy., pp. 377-
386, 1974.
Gold, B., and C. M. Rader. Theory and Application of
Digital Signal Processing. McGraw-Hill, New York,
1969.
Gold, B., Lebow, I. L., Hugh, P. G., and C. M. Rader. "The
FDP a Fast Programmable Signal Processor." IEEE
Trans. Computers, C-20:33-38, 1971.
Gotman, J., and P. Gloor. "Clinical Applications of Spec
tral Analysis and Extraction of Features from Electro
encephalograms with Slow Waves in Adult Patients."
Electroenceph. Clin. Neurophysiol., 35:225-235, 1973.


97
The most striking are the following: definition of begin
ning and end of seizure, uncertainties related to the
fading of the pattern in the middle of an ictal discharge
(single seizure?), modifications of the nature of the pat
tern to polyspike and wave or only slow waves (should the
count be terminated and restarted?).
It is interesting that only one paper was found which
dealt exclusively with the morphology of the PM wave com
plexes. This advanced the idea of trying not only the
detection of the PM paroxysms but also their analysis.
Weir (1965) analyzed, using a storage scope, the morphology
of the spike and wave complex and concluded that "they are
composed by a small short duration negative spike followed
by a prominent positive transient from which the second,
larger amplitude negative spike originates. The negative
wave that follows is not a complete dome but approximates
the first three quarters of one (Fig. 10)." He points out
the masking effect of the EEG recording time constant for
the lack of widespread recognition of these elements. He
characterized the complexes as follows: Spike one is small
amplitude (25-50 yV), negative and of short duration
(10 ms). It has a triphasic potential when considered with
the preceding activity. The positive transient is a sharp
positive deflection with duration of 100-150 ms. Spike two
appears in the positive portion of the complex and was gen-
erally of high amplitude (100-200 yV) and with duration
between 40 and 90 ms. The amplitude of spike two waxed and


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Graduate Research Professor of
Psychology
This dissertation was submitted to the Graduate Faculty of
the College of Engineering and to the Graduate Council, and
was accepted as partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
August 1979
Dean, College of Engineering
Dean, Graduate School


131
The weight attributed to them will be reduced in this work.
There was even an attempt of designing the slow-wave detec
tion without an amplitude threshold, but surprisingly there
was a lot of EEG activity detected as shown in Fig. 18.
When an amplitude threshold of 25 yV was utilized, the only
activity besides PM detected in the awake records was the
eye movements. In the neurophysiology literature the
amplitude of the slow waves is said to be at around 100 yV;
hence, it was decided to increase the threshold to 75 yV.
It is here acknowledged the desirable effect of increasing
the threshold for the rejection of high energy artifacts.
The amplitude of the spike threshold was also set at
75 yV. The importance of this threshold is higher than for
the slow waves, since the only other parameter used to
detect the spike transient is the period. This value dis
plays a good rejection to most of the muscle activity
present in the EEG when the subject is not moving around.
The recordings were obtained with the patients awake for
the great majority of the time, and therefore the EEG is
expected to be contaminated with muscle activity. Fig. 19
shows a typical performance of the detector in a muscle
contraction, subject not moving.
One other problem faced was the determination of the
amplitude levels at the filter output, since these filters
possess gains greater than one. The microcomputer and its
arithmetic facilities enabled an elegant solution. In the


112
other parameters of the digital waveforms are necessary,
like peak amplitude or slope measurements, because for
interpolation every parameter utilized needs a reconstruc
tion method.
For the detection parameters that are sought a sampling
frequency of 240 Hz seems a good choice, since the preci
sion on the period measurement of the spike is kept around
1 Hz (10 percent), and the peak amplitude can also be
determined with a reasonable accuracy. The other variable
that controls the choice of the sampling frequency is the
frequency content of the data. The concern is not the
accuracy of representing the EEG waveforms but the aliasing
effect of muscle activity. It is known that electrical
potentials from the cranio-facial muscles have frequency
components up to 150. Hz (Smithy 19.79)., while for the .
EEG the frequency content can be assumed below 40 Hz. For
the representation of muscle activity a sampling frequency
of 300 Hz would be necessary, but the sampling frequency
can be selected below this quantity as long as the muscle
components are folded back to a non-EEG frequency range.
For the numbers given above, any sampling frequency above
190 Hz will accomplish the folding to a non-EEG range.
This fact is shown in Fig. 13.
Selection of the PM Filters Characteristics
The purpose of using EEG linear filters in the EEG
detection is to attenuate out-of-band activity. Care must


I
272


25 yV
Fig. 18. Slow Wave Performance. No Threshold.
132


328
TITL ,oL0T *
44 4# #*.4.4 44 4444444 4 4444 44 44444:44 444
* PLOT
4444 444 4 44 *44444 4 4444 444 4 4 44 44 444
* MODULE THAT DISPLAYS POSITIVE
* DATA INTO THE TEXT 611 DISPLAY
*

X
DATA
I S
ASSUMED
I N
RO
*
M A X X
It
ft
It
R 1
*
Y
DATA
ft
It
W
R2
4
MA X Y
Vt
t
n
R3
4
X
AXIS
IS
D/A I
4
* REG 9 IS D/A CONVERTER POINTER
* REG 10 IS EASE ADDR
* REG 12 NEEDS TO BE LOADED WITH
* BEGINING ADOR CF PLCT+39A
*
* SEE DATA PROGRAM FOR CONSTANT DESCRIPTION
*
2200. AORG >2200
1 EFO
ADCX
EQU
' >1EF0
1EF2
ADCY
EQU
>1 EF2
FCOA
CONST
EQU
>F C04
FC06
OLDX
EQU
>FC 0 6
FC 03
CLDY
EQU
>FC0 8
FCOA
NEVrX
EQU
>F COA
FCOC
NE'rt Y
EQU
> FCOC
FC OE
XDIF
EQU
>FC0 E
FC10
YD IF
EGU
>FC 1 0
FC12
MASK
EQU
>FC12
FC 1 A
SCALE
EQU
>FC 1 4
FC 16
LIM
EGU
>FC 1 6
22 0 0
C12A
MOV
2>l 0 CIO )
,4
R4 GETS
XO
2202
00 10
220 A
CA44
MOV
4,32C9)
OUTPUT
xo
2206
0 0 02
2203
C 644
BACK
MOV
4, #9
OUTPUT
YO
220 A
06 9C
BL
*1 2
INTENSIFY BEAM
220C
0 5 84
INC
4
220 E
8 A34
C
a, a>12c i
0)
PEACH THE
END?
2210
00 12
22 12
1 5F A
JNE
BACK
221 A
Ci 2A
MOV
2> 1 0 C 10 )
,4
PLOT Y
AXIS
2216
00 10
2218
C644
MOV
4 ,*9
221 A
CA44
EAQ
MOV
4,32(9)
22 1C
0 0 02
221 E
0 69C
BL
4 12
2220
0534
INC
4


Fig. 31continued
173


TABLE VIIcontinued
PATIENT #16
Session
(EEG Mon
tage)
Repetition
Period (sec)
Half Period
Slow Waves
(sec)
Delay Slow
Wave Spike
(sec)
Filtered
Slow Wave
Amplitude
(yV)
Filtered
Spike
Amplitude
(yv)
In Sz
In^sT
Sessiori\^
X
a
X
a
X
a
X
a
X
0
\ 0.13
\ 0.03
\ 0.11
\ 6.08
V 5.83
1st
V1,
0.37
0.7o\
0.12
0.04
0.19
0.1l\
141
5.54V
128
4.6S\
\ 0.10
\ 0.04
\ 0.38
\ 5.08
\ 3.86
2nd
0.31
0.13
\
0.17
122
106
\
0.12\
0.04\
0.2l\
7.27\
6.6r\
3rd*
\
\
*Bad tape
196


152
was implemented. Instead of performing the shifting before
the division by N, it seems equally time-consuming, but
much simpler, to perform an extra division using the
shifted left remainder. Proper care was taken to shift
equivalently x.
2
It may happen that Ex^ is so big that the division by
N will yield a number greater than the maximum represent
able number in a 16 bit machine. In cases like this, the
number of occurrences (N) is shifted left 4 bits, and the
variance is then calculated with a magnitude of one hexa
decimal digit smaller. Although this operation degrades
the resolution, it is the only way to perform the computa
tion in fixed point.
FILTER. This is the module that performs the fourth
order bandpass filtering in the range 10-25 Hz and 0.8-6 Hz
with sampling frequencies of 240 and 80 Hz respectively.
Control is passed through a BLWP using register 8, 9 of
MAIN. The modules are 4 independent workspaces (one for
each resonator). A detailed description of the filter
program is given in Appendix II. When control is passed to
FILTER, there is a wait loop which synchronizes program
flow and the sampling frequency. Control leaves the loop
through a level III interrupt. The 80 Hz sampling fre
quency is obtained by calculating the filtering for every
one out of three input points.
INTHAND. This module sets the sampling frequencies
through an interrupt. The TMS 9901 is used as a timer, and


226
with automatisms that produce muscle potentials (e.g., eye
blinking, teeth grinding). The inclusion of further proc
essing channels to use the bilateral synchrony property of
the PM pattern also fails, because chewing is also syn
chronous in the frontals. Of course, a brute force solu
tion is to include a push button on the detector which will
disable the seizure detection. However, this may lead to a
lot of errors (accidental triggering, forgetting to push
the button, etc.).
The inclusion of the statistics as'an output and the
constancy of the PM parameters suggest another method to
deal with the problem. Only by chance does the chewing
possess the same characteristics as the PM patterns; there
fore, further processing of the statistics data may elimi
nate the false detects in chewing (and the other types of
artifacts). The most sensitive parameters seem to be the
repetition rate and its variance. Figs. 49a and b show
examples of false positives in the plot time of occurrence/
repetition rate/variance of repetition rate for patients
#7-1 and #7-2 and Fig. 49c for patient #12-1. The problem
as enunciated is a classical communications problem:
knowing the a priori probability of false detection (from
the evaluation) and assuming gaussian probability density
functions for the detection, a boundary can be easily eval
uated with the seizure data (Helstrom, 1964). Additional
information can be supplied taking into consideration the
fact that no false detections greater than five seconds


276
23AE
2 3B0
FC00
1 504
JGT
CLEAR
2382
0203
LI
3 > 140
YES.LOAD SAFE VALUE
23B4
228 6
2383
238 A
0140
C803
FCOO
0581
CLEAR
MOV
I NC
3.3DELAY
l
INC R. RATE COUNTER
2 23 C
C 0 41
MOV
1 1
OVERFLOW (NEG)7
23 BE
22C C
1502
0201
JGT
LI
OKAY
1>140
LOAD SAFE VALUE
22C2
23C4
0 1 40
04 07
CKAY
LVKP
7
GET DATA POINT
22C 6
C802
MOV
2 *2> 1 EFO
OUTPUT IT
23C8
2 3CA
1 EFO
CAEO
CLP
3>1EF2
CLEAR D/A II
22CC
23CE
1EF2
0208
L I
3. >208C
SKIP INITIALIZATION
2 2D0
2 20 2
20 8C
0405
BL'aP
5
GO TO SPIKE
2304
C 002
MOV
2.0
GET SIGN CF INPUT
220 6
2308
230 A
22DC
230 E
23E0
4020
FC06
0280
8000
16E2
C0C2
4
*
*
NEG
SZC 3MASK.0
c.i o,>aooo
JNE PEAK
1ST LOOP
MOV 2 ,3
SAVE DATA IN R3
22E2
0581
INC
1
INC R. RATE COUNTER
23 EA
05 AO
INC
3DELAY
INC SPIKE DELAY
2 2E6
23E3
23E A
23EC
2 3EE
23F0
FCOO
0407
caoa
1 EFO
0405
S0C2
8L WP
MOV
BLViP
C
7
2,3>1EF0
5
2. 3
REACH NEG PEAK?
2 2F2
2 3F4
2 3F
13F6
1 1F5
04 C4
JEQ
JLT
CL R
NEG
MEG
4
YES CLEAR VAL-PEAK COUNTER
23F 8
04C9
CLR
9
CLEAR ZERO CROC COUNTER
2 3F A
C303
MOV
3.12
SAVE VALUE OF VALLEY IN RI2
2 3FC
C0C2
*
*
CUME
2ND LG
MOV
CP
2 .3
2 3FE
2400
2402
2404
2406
24CS
240 A
240 C
C 584
0581
C5A 0
FCOO
0407
C 8 02
l EFO
0405
I NC
INC
I NC
3LWP
MOV
QLWP
4
1
3DELAY
7
2 3>1EFO
5


39
bandpass filters (Smith, 1978). The present design uses a
slightly underdamped frequency response. It is hard to
qualify the desirable properties of the filters since there
is no general theory of EEG detection. The only possible
criteria are to understand the filter function in the
detection scheme and hopefully arrive at some rules that
will serve as guidelines for filter selection.
The purpose of using EEG filters in sleep studies is
to attenuate out-of-band activity to enable further signal
processing (e.g., zero-crossing). On the other hand, the
filters shall not mask out-of-band activity so that it will
look like in-band activity for the rest of the processing
algorithm. Every filtering function produces a certain
masking, since the filter output is the convolution of the
filter's impulse response with the input. However, the
weight of the smoothing is controlled by the Q of the fil
ter, hence the use of low Q filters. At present no other
characteristics of the filters, like phase distortion or
group delay, have been brought into the picture of filter
selection (Smith, 1978). The in-band amplitude character
istics have also been neglected due to the wide variability
of the amplitude of the EEG. The above-mentioned analysis
refers to EEG sleep studies. For the epilepsy application
the knowledge is still less quantitative due to less expe
rience From the study of the petit mal pattern it can be
concluded that the fast attenuation characteristics are of
paramount importance for the slow wave filter (activity as


Fig. 15d. Spike Impulse Response.
256 Points.
124


44
s
2 z-1
T Z+l
(6)
The particular type of isomorphism (an infinite length line
mapped into a finite line) implies a nonlinear mapping, in
the sense that a Az has different correspondence to a Aw,
depending on the value of z. As a matter of fact, the
transformation follows a tangent rule as can be easily
shown (Oppenheim & Shafer, 1975). Therefore, to get the
correct frequency characteristics in the Z domain, the S
plane filter critical parameters (center frequency, band
width) have to be properly prewarped (Childers & Durling,
1975). Nevertheless, a piecewise linear response is mapped
onto a piecewise linear response, preserving the boundaries.
It is important to point out that the prewarping does not
change the nonlinear properties of the transformation, but
compensates for it. So a distortion of the phase response
of the filter will always be present.
One of the most interesting properties of the bilinear
transform is the absence of aliasing. The theoretical
explanation is very easily understood. As the entire jw
axis is mapped onto the unit circle, the folding frequency
(z=-l) corresponds to w=, and the attenuation of any
realizable network shall also be infinitely large. How
ever, from the Z domain point of view the reasoning does
not seem explanatory since the Z axis is the same whether
the filter is mapped using a rational or a nonrational
transformation. In the particular case of a filter, the


ACKNOWLEDGEMENT S
The author would like to thank his supervisory
committee for their aid, guidance and criticism during the
preparation of this dissertation. Especially the author
would like to thank Dr. Jack Smith for his willingness to
share facilities, personal contacts and responsibilities.
It was an unconventional but effective learning experience,
which went beyond the restricted field of EEG studies. The
friendly relationship created during these years is deeply
appreciated.
There are many others who contributed their knowledge,
skills and time for this dissertation to become a reality.
The author would like to thank Sonny, Yvonne, Shiv, Nate,
Dan, Alan and Salim for their large, small, direct or
indirect contributions. Special thanks go to Fred for his
constant help-in the data collection phase.
The author also would like to thank the Department of
Electrical Engineering of the University of Florida,
Comissao Permanente INVOTAN (NATOPortugal), and the
Institute of International Education for the financial
support received throughout his graduate studies.
The author sincerely thanks his family for their sup
port and confidence, especially his wife for her constant
ii


158
TAPE RECORDER
Procedure:
1 Tape Recorder to Record Mode
2 Extension Port Switch to Reverse
3 Press Y Key in Terminal (after
10" of Leader)
4 When Finished Switch to Neutral
. 28. Record from Microcomputer to Tape Recorder
Fig


33
available. This fact per se has the potential to expand
the field of application of digital filter signal proces
sing. This approach is also less expensive since the
machine may be a general purpose computer, and so there is
no extra cost involved in the new application. The draw
back is the computer's fixed architecture which is not
adapted to calculate recursion relations.
For a lot of applications the requirements of the
implementation can be met with mini-computers and even
microcomputers. The principal elements of the requirement
set are speed, type of arithmetic, wordlength. Digital
algorithms work in digital representations of real world
(analog) signals. It is well known (Thomas) that to make
a digital representation of an analog signal unique (i.e.,
the analog signal can be reconstructed again from the
digital samples) a maximum frequency must be assumed in the
signal spectrum. This is the same as saying that the time
domain representation of the signal is restricted to change
at less than a prescribed rate, governed by the time/
frequency inverse relationship. The theorem that relates
the uniqueness of the digital representation and the
sampling frequency is the Nyquist theorem, and it imposes
a lower bound on the sampling frequency (sampling frequency
equal to two f^). This theorem assumes two impossibilities:
first, that the signal spectra are frequency band limited,
and second, that the past and future history of the signals
are completely available for reconstructing the analog


345
Walter, D. 0., Kado, R. T., Rhodes, J. M., and W. R. Adey.
"Electroencephalographic Baselines in Astronaut Candi
dates Estimated by Computation and Pattern Recognition
Techniques." Aerospace Med., 38:371-376, 1967.
Walter, D. 0., Muler, H. F., and R. M. Jell. "Semiauto
matic Quantification of Sharpness of EEG Phenomena."
IEEE Trans. Biomed. Engng., BME-20:53-55, 1973.
Weinberg, L. Network Analysis and Synthesis. McGraw-Hill
Book Co., New York, 1962.
Weir, B. "The Morphology of the Spike and Wave Complexes."
Electroenceph. Clin. Neurophysiol., 19:284-290, 1965.
Welch, P. D. "The Use of FFT. for the Estimation of Power
Spectra. A Method Based on Time Averaging over Short
Modified Periodograms." IEEE Trans. Audio and Elec-
troacoust., AU-15:70-73, 1967.
Wennberg, A., and L. H. Zetterberg. "Application of a Com
puter Based Model for EEG Analysis." Electroenceph.
Clin. Neurophysiol., 31:451-468, 1971.
Wilder, B. J., Willmore, L. J., Villarreal, H. J., Bruni,
J., and R. J. Perchalski. "Valporic AcidAcute
Study." Published by Epilepsy Research Foundation of
Florida, Inc., 1978.
Woody, R. H. "Interjudge Reliability in Clinical Electro
encephalography." J. Clin. Psychol., 24:251-256,
1968.
Yeo, W. C. "A Signal Detection from Noise Utilizing Zero
Crossing Information." Ph.D. Dissertation, University
of Florida, 1975.
Zetterberg, L. H. "Estimation of Parameters for a Linear
Difference Equation with Application to EEG Analysis."
Math. Biosci., 5:227-275, 1969.
Zetterberg, L. H. "Spike Detection by Computer and by
Analog Equipment." In Automation of Clinical Electro-
encephalography. Raven Press, New York, pp. 277, 234,
1973.


134


130
wave complex was the only parameter, it would be very
difficult to implement the desynchronization of the pat
tern. The detection being a two-stage process, it is
possible to acknowledge the presence of slow waves even
when they do not appear with the prescribed repetition
rate, as may happen in the middle of the seizure. This
feature enabled the recognition of desynchronizations with
out breaking the seizure in two separate events.
Period Window for the Spike
As it was pointed out earlier, one of the spikes
(second) present in the PM pattern is relatively slow and
of very high energy. The first spike individualized by
(Weir, 1965) will not be detected here. To detect most of
the second spikes present in the beginning of the PM parox
ysm a time window of
0.09 sec (Ajj)
to
0.05 sec (6h)
corresponding to 11-20 Hz was necessary. It avoids detec
tion in alpha bursts.
Amplitude Thresholds
Previous work in sleep research has shown the incon
sistency of amplitude measures for EEG signal detection.


53
decrease it, scaling can be utilized at expenses of dynamic
range, or for some cases an alternate transformation can
give smaller gains. The other possibility is to decrease
the sampling frequency, making the filter appear wider and
therefore lowering the Q. Although for certain areas like
speech processing this is not of great practical value, for
EEG it is a viable procedure, since the EEG rhythms can be
considered not coupled. The penalty paid is higher compu
tation time as a digital lowpass filtering shall be per
formed before the reduction of the sampling frequency to
avoid aliasing. Peled (1976) has a detailed analysis of
the procedure including setting of lowpass corner frequency
and new sampling frequency.
The rationale for using lowpass FIR filters is the
following: If decimation is desired (lower sampling fre
quency at the output), only the samples which will be used
need to be computed. In the case of FIR filters, where the
output is only a function of the past values of the input,
this can be accomplished easily. For HR filters the
present output is a function of past values of the input
plus of the output, which means that every point must be
computed. The threshold where the FIR filter is prefer
able to the IIR is given by the ratio of decimation and the
difference in filter order to keep similar attenuation
characteristics.
An automated procedure to design IIR bandpass
Chebyshev filters has been presented. It was shown that


FREQUENCY ANALYSIS NODE HUNtiEH 16
MAGNITUDE
60.01599.. **
Ht Ir
K a
-il 1! I:
CHEYSMEV 41H ORDER IMPULSE 1NV. BANDPASS
C2. 02. 11 ¡ C 1, D1 1 SLUM NAVE
54. 014B9.
43. 01379.
42. 01270. .
36. 01160.
30.01050.
24.00940.
18. 00330.
12. 00720.
6. 00610
0. 00500.
*** it
funs*********#*****###***##**#**.
O. 10E-0J O 79E OI O. J6E 02 O. 24E 02 O. 32E 02 O.40E 02
O. 40E 01 O. 12E 02 O.20E 02 0 SHE 02 O. 36E 02
FREQUENCY (IITZ)
CO
00
Fig. 9c. Filter Frequency Response (Slow Wave)


110
Referring to Fig. 12, the equation of the straight line
is
2~Btl + B+A t
t^+t2 t^+t
(49)
where
A = -M sin wt^
and
B = M sin wt2*
For y=0 (zero crossing)
E = Btl~At2 (50)
B+A
To find the maximum of (50) with respect to t2* the follow
ing substitutions of variables were made.
0 = t2~T/2 and a = T/2.
So (50) becomes
e = 0-a cotg(wa)tg(w0).
(51)
The maximum is
-!§ = -14 = 0 -* cos^w0 = aw cotg wa
O t o Op
fc2 = § + £ cos"1 ( |w cotg (2^)) .
(52)


108
It is also desirable to build a system which will be
repeatable, since the advantages of microcomputers may
very well broaden the number and areas of application of
the system.
The choice of the implementation media imposes a
strong bias in the detection methods. It is felt, however,
that this does not necessarily mean constraining the detec
tor performance, as will be exemplified. It just means
that certain possible ways of extracting the information of
the basic PM components will not be applied here. For
instance, if the frequency information of the basic
recruiting rate is desirable, time domain techniques (like
zero-crossing, or peak detection) will be preferred to the
frequency domain analysis, like FFT. When the character
istics of the PM paroxisms were summarized, some highlights
about the extraction of the parameters were introduced.
Here the complete detection scheme will be analyzed.
Sampling Frequency
The first building block of the detector is the A/D
converter, since the entire detection process will be
realized in the digital domain. One of the most crucial
parameters to be set is the sampling frequency. For EEG
signals the frequency content may be set at 40 Hz even for
abnormal EEG, since Smith (1974) found no modification in
the spike characteristics used for detection when the data
were prefiltered at this frequency. However, when the


100
The slow wave detection that will be used here is
adapted from the detection of delta waves in the sleep
studies. Basically it consists of a bandpass filter
0.8-6 Hz, 12 dB/oct, and amplitude and period detectors.
Spike detection is a very difficult problem. The
methods employed so far, besides the computationally expen
sive amplitude-duration criteria, rely on the sharpness as
the main parameter. They are, however, sensitive to the
muscle artifact (see literature survey). As the spike is
not a very reliable parameter during the PM paroxism, not a
lot of effort was directed towards its detection. One
approximate model for the spike is a triangular wave. From
the Fourier transform of a triangle, most of the energy can
be expected at the fundamental frequency (the even harmon
ics are zero, and the third harmonic is 1/9 of the funda
mental) From the definition of the spike duration, the
fundamental frequency will be between 12 and 20 Hz. Hence,
a crude spike detector will be a bandpass filter from
12-25 Hz, 12 dB/oct to extract most of its energy, followed
by a zero-crossing analysis of the filtered data to separ
ate other EEG activities which will have appreciable energy
in the frequency range (e.g., alpha wave bursts). The
effect of muscle artifact will be minimized since most of
its energy is contained above this region (O'Donnell et
al., 1974).
The next step is to combine the information of the
detectors to reach a pattern recognition algorithm. It is


Update
mem. pointer




2
descriptor of the EEG parameters. At the present time this
is a very hot topic where one can read reports that show
the short time stationarity of the EEG for sequences below
20 seconds for a probability of error of 10 percent (Cohen
& Sanees, 1977; Kawabata, 1973; Saltzberg, 1972). However,
the work of Elul (1967, 1969) and Dumermuth (1968) points
out the nonstationary behavior of EEG sequences as short as
4 seconds. Another important characteristic, albeit less
addressed, is the Gaussianity of the EEG. The work of Elul
(1967, 1969) and McEwen and Andersen (1975)' suggested that
the behavior of the EEG followed a Gaussian distribution
32 to 66 percent of the time depending upon the behavioral
state of the subject (active mental task to relaxed state,
respectively). It also displayed a spatial distribution
with closer Gaussian characteristics in the occipital
leads. Some of the discrepancies that are reported in the
literature can be explained by the different sampling rates
used in the A/D conversion, since oversampling may distort
the local statistical properties of the digital waveforms
(Persson, 1974). Another reason, and maybe more plausible,
just demonstrates the variability of the EEG with subject
and behavioral state.
In practice 'the stationarity requirement can be loos
ened to stationarity during the observation period, and if
the process departs slightly from Gaussianity, ancillary
parameters like skewness and kurtosis could be employed
along with spectral analysis. If stationarity holds, but


24
integrated amplitude from a combination of 4 EEG channels
to detect PM activity. The system stores the duration
and time of occurrence of the seizure. The overall agree
ment, consensus versus machine, is 85 percent. It is, how
ever, interesting to note that in the paper's extensive
discussion, no mention is made on artifacts that may cause
potential problems like chewing and body movements, which
suggests that the investigators had available rather clean
data. The system is reported to be sensitive to slow wave
sleep. Carrie and Frost (1977) also described a spike and
wave detector. It is composed of a spike detector, using
the sharpness criteria (Carrie, 1972a), an EMG detector and
an information of the amplitude of the background activity
(Carrie, 1972b). One channel is analyzed on line, and the
system stores the duration of the paroxism and its time of
occurrence. The agreement is very high for seizures
greater than 3 sec (85 percent) but drops off to 25 percent
for Sz between 1-3 sec. The patients were reported to have
well-defined PM paroxisms and were free of medication.
From the EEG data available to us it seems that the large
amount of high energy artifacts that resemble the PM pat
tern when the patients are in an unrestrained environment
dictates the use of more powerful pattern recognition algo
rithms.
Johnson (1978) implemented in a microcomputer a PM
detector based on the repetition properties of the pattern,
i.e., spikes followed by slow waves. He used two analog


1.5 hour
i
V
I-
Fig. 38. Spike Amplitude Versus Time (#12-3)


225
Fig. 48a. Chewing No Detections


149
wave reaches the peak, tests on the valley-to-peak ampli
tude and period are made. If any of these conditions
fails, control is passed to the beginning of the PEAK pro
gram. Otherwise, the time to reach the next zero crossing
is monitored (R9). If it is within limits (only a positive
threshold is tested), a slow wave was recognized and the
values of peak amplitude and 1/2 period (valley-to-peak)
are transferred to STATIS. A negative pulse is outputted
to D/A II to signal the detection of a slow wave, and con
trol is passed to MAIN to check the repetition rate.
SPIKE. This program has an independent workspace and
is linked through a BLWP using R5, R6 of MAIN. Valid data
appear in R3. The first loop looks for a zero crossing -
to +. As this program has three basic loops, it has to be
indicated to PEAK in which of the three loops is the pro
gram control, before jumping back. This was accomplished
by loading the value of the PC for the next sample in R6 of
MAIN.
When the zero crossing is detected, Rl is cleared, and
the program looks for the peak of the activity. In the
next sample control enters the third loop that looks for
the next zero crossing. When found, the program tests the
period and amplitude requirement. If met, the amplitude
and the value on DELAY (number of points between last slow
wave peak and spike peak) are transferred to STATIS; the
spike recognition location (DELAY) is cleared; and a posi
tive peak is outputted to D/A II.


280


93
since the noise created will appear without attenuation at
the output. If the poles have approximately the same Q,
the pairing is the more determining factor. Nevertheless,
the combination which gives the highest magnification shall
be realized first, but it may not be apparent from inspec
tion.
Supposing that none of the combinations can be imple
mented with the available hardware (i.e., A/D and microcom
puter) before setting for a change in the hardware, the
following should be attempted: Design the filter with
another transformation (wide-band), and decrease the
sampling frequency (decimation). If all the above fail,
then the only thing left is to scale the signals between
resonators. The second method is the only one that does
not sacrifice output signal to noise ratio. Scaling
between resonators is probably the one that most deterio
rates the signal to noise ratio, since it is done in a
place on the structure where the noise is far from being
white. Hence, scaling between resonators means reduce the
noise power less than where the noise is wide-band (inter
nal nodes of structureJackson, 1970). However, it can be
accomplished with only one shift operation.
As a concluding remark it is felt that the design pro
cedure described is of practical value for EEG signal
processing. From the topology point of view the most
stringent constraint is the number of multipliers. It is
felt that even with the practicability of the design


325


170
System Evaluation
The group of patients for the drug study was purposely
chosen to be medically refractory to other drugs. They
were under heavy medication, and for the most part they had
a long history of generalized seizures. It was also common
to find patients with mixed seizure types (myoclonic or
focal). Since the detector has built in specifically a
scheme to detect PM seizures, a selection of the patients
was judged appropriate to test the PM model implemented.
Another reason for the selection can be found in the effec
tiveness of the drug, since most of the patients had a
total reduction of clinically significant seizures. So no
paroxisms will be found in most of .the post-drug records.
As stated in Chapter III, the detection criteria were
chosen to apply to the classical PM and PM variants. A
group of four patients was selected to be used in the set
ting of the detection parameters. The group was formed by
patients
#3 PM variant
#7 classical
#12 classical
#21 PM variant.
Examples of their patterns have been presented in
Figs. 11a, 27a, 27b, lid. Portions (30 minutes long) of
the tapes containing paroxysms were re-recorded and used in
the detector calibration. Needless to say, in this group


18
can be inferred. Isaksson and Wennberg (1976) point out
that about 90 percent of the records of 20 s are stationary
which agrees with some of the previous observations. At
the present time, only Isaksson (1975) and Isaksson and
Wennberg (1976) have used this technique.
Time Domain Approach
If one can relate the degree of quantization to the
maturity of a field of science, electroencephalography is a
newborn. The lack of quantization has two main conse
quences: the inexistence of objective criteria to charac
terize the EEG phenomenon that weakens any purely analytical
research method (like spectral analysis); the resort to a
multitude of soft criteria (i.e., not unique), each based
on empirically derived parameter values that try to trans
late the highly nonlinear way the electroencephalographer
reads the EEG.
Visual analysis is a true time domain method of detec
tion of structural features like diffuse and localized
change in frequency and voltage pattern, changes in the
topographic distribution and in the interhemispheric sym
metry, sharp and rhythmic activity, paroxysms and unstable
or irregular time course. The basic patterns and clinical
EEG features are composed on the following step-by-step
procedure: the analysis of the period and: amplitude ..
forms the wave concept that is associated with the gradient
to give the simple grapho-element. These can be integrated


198
The data available to us had unfortunately too many
variables to permit conclusions considering the comparison
of pre- and post-Depakene administration. The problem is
the use of different EEG montages. As can be seen from
Table VII, different montages were utilized to record each
session. There have been reports of parameter dependency
with EEG montage in normal activity (Smith, 1978), and in
PM it is well known that the amplitude of the slow wave
varies with the electrode location. For this reason it is
impossible to couple the increase in the repetition period
for the third session of patients #3, 4, and 7 with
Depakene administration. However, with a more careful data
collection this question can be easily answered with the
present system, as long as the false detections are
excluded (not to bias results as in the case of patient
#5-2.)
Another bit of information which can be obtained with
the new instrumentation system is the correlations between
PM parameters to quantify in more detail the PM phenomena.
With the set of data available the following problems
should be considered: first, the small data set; second,
the existence of a number of uncontrolled variables, such
as seizures occurring in different physiologic states
(sleeping, awake, medication), utilization of different EEG
montages, and all the seizure detections considered
(including false positives). Therefore, a nonrigorous


275
TITL PEAK*
** 3jt* *** *5* #*##3:*5}:3¡!*
* PEAK PROGRAM
******* ***.*;** *:*:£#*****#**
* MEASURES VALLEY TO PEAK
* PERIOD ANO AMPLITUDES IN '
* SLOW WAVE FILTERED DATA.
* IT ALSO CHECKS ZERO
* CROSSINGS (MAX LIMIT)
* THESE PARAMETERS ARE PASSED
* TO ST AT IS
* NEG PULSE IN D/A II WHEN S.W.
* IS RECOGNIZED
*
* CONTROL IS PASSED TO MAIN <3L)
* INPUT,SPIKE AND STATTS (SLWP)
*
*REGI
*
*
*
*
*
*
*
STER3 USED
RO SIGN OF INPUT
RI R. RATE COUNTER
R2 INPUT DATA
R4 VALLEY TO PEAK COUNTER
RS,6 SPIKE LINK
R7.Q INPUT LINK
R9 ZERO CROSSING COUNTER
R 12 AMPLITUDE
20A 0 AORG >23AO
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23 AC
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KEEP S IGN IN R4
INC SPIKE DELAY
OVERFLOW(NEG)?


025 sec
Fig. 42b. Half Period Versus Duration (#12-3)
216


Microcomputer System
Fig. II-l. TI 9900 Microcomputer Block Diagram
252


37
number of operations, providing at the same time good
overflow and noise properties.
To design a filter with a specific output signal to
noise ratio using the minimum requirements of computation
wordlength and processing time, the following factors need
to be analyzed:
1) Filter transfer function
2) Filter internal magnification
3) Noise characteristics of filter topology
4) Processing speed.
The problem as enunciated is relatively different from
the design procedure commonly found in the literature,
since there the optimization is studied with respect to
only one parameter (most generally to sensitivity to round
off) neglecting any other considerations. It turns out
that the optimum structures possess a much higher number of
multipliers which will mean slower computation time in our
application. Examples are as follows: The synthesis of in
finite impulse response filters (HR) with low roundoff
noise based on state space formulations has been presented
by Hwang (1976) and Mullis and Roberts (1976). Their struc-
2
tures have N more multipliers than the canonical structures,
where N is the filter order. Another example will be the
structure proposed by Barnes et al. (1977), which is free
from overflow oscillations, but requires N+l more multi
pliers than the canonical structures. Multiplier extrac
tion was also considered (Szczupack & Mitra, 1975),


False
Detection
tan
o
*
Fig. 49c. Mean and Variance of Repetition Period Versus Time (#12-1)
08 sec 0.639 sec


284
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0281
Cl
1 LRATE
2500
0005
2 50 2
1 ICC
JLT
BACK
2504
C820
MOV
3DELAY,3WSTA3 PASS DELAY SPIKE S.W.
2 50 6
FC 00
2508
FDEO
2S0 A
C302
MOV
2.3WSTA5
PASS SPIKE AMP TO STAT
2 50C
FE2C
250 E
04E0
CLR
2DELAY
2510
FC 00
2512
0420
BLV*P
3STAT3
251 4
F Cl 6
2516
C 420
3LWP
3STAT3
2518
FC IE
251 A
02 04
LI
4,>7FF
OUTPUT + 3UL SE TO 0/A
251 C
0 7FF
251 E
C804
MOV
4,3>1EF2
2520
1 EF2
2522
1 08C
JMP
SACK
2524
1000
NOP
END
NO GF
ERRORS IN
THIS A 3SE
VBLY= 0000
RELOCATABLE LOCATIONS USED = 0000


38
but the structures obtained lack the optimum sensitivity
characteristics. Another interesting idea is presented in
Chang (1978), where the decrease in the roundoff noise is
accomplished by feeding back the discarded bits, properly
weighed, to the input of the adder following the place
where the product is quantized. This procedure doubles the
multiplier number. Szczupahk.and Mitra (1978) propose the
reduction of the roundoff noise by ensuring the presence of
zeros in the noise transfer functions. This procedure
leads to zeros that are complex, therefore requiring extra
multipliers for its realization. Many more examples could
be given, but the picture remains unchanged; decrease of
roundoff noise means more multipliers. For a microcomputer
implementation of digital filters multiplication is by far
the most time-consuming operation, and it is therefore
necessary to minimize its use. It seems appropriate to say
that for microcomputer implementation a suboptimal solution
would be the best, weighing the effect of the increase in
computation time and the decrease in the variance of the
output noise. This analysis is not known to exist, so the
procedure chosen utilized canonical structures as well as
slight variations in their topology (adders as a variable).
Filter Transfer Function
The characteristics of the filters presently used for
sleep EEG studies have been obtained through trial and
error. Basically the filters are low Q, second order


157
310, appearing respectively in memory locations
FC2A, FC2C, FC2E.
Testing of the Program
The efforts undertaken in the program modularity were
rewarded in the testing phase.
A brief description of the facilities available is
thought helpful at this point. To write the programs in
assembly language the cross assembler resident in the
Amdahl 470-V6 was extensively used. The editing facilities
of the operating system and the error messages of the cross
assembler were thought adequate for the software develop
ment. The same feeling is shared with the cross assembler
resident in the NOVA 2/10. The program loading in the TI
microcomputer from any of the computers was performed auto
matically through the resident TIBUG monitor (LOAD command)
via a Modem (Pennywhistle 130). To get a permanent copy of
the programs after being loaded in RAM memory a REALISTIC
cassette recorder was used, along with the DUMP command of
the TIBUG monitor, and a Modem. Fig. 29 shows the respec
tive connections. Care must be taken in the volume and
tone setting in the cassette recorder. There were no relo
catable facilities in the monitor; therefore, only absolute
origins were used in the assembly programming.
The debugging of the program functions was not as
easy, first, due to the complexity and dependence of the
program flow in the input data, and second, due to the poor


240
w
Passband
Trans. Attenuation
Band Band
Fig. I-I. Chebyshev Low Pass Characteristic


96
discharges, that is, paroxysms with duration greater than
3 seconds.
In PM epilepsy the paroxysms are spike and wave com
plexes. A complex is a group of two or more waves clearly
distinguished from background activity and recurring with
a well-organized form. The spike has a duration of 1/12 of
a second or less, and a wave has a duration of 1/5 to 1/2
second. The spike is usually biphasic and has a preva
lently negative polarity. The amplitude is generally
greater than that of background activity and averages
50-150 yV. The wave is a sinusoidal-type waveform with
medium to high negative voltage that averages 100 yV. The
spike can be less apparent or be substituted by polyspikes.
In PM epilepsy the wave complexes appear predominantly in
the frontal leads and are bilaterally synchronous and sym
metrical, recurring rhythmically at about 3 c/sec (faster
in the beginning of the seizure, 3-4 Hz, and slowing down
toward the end, 3-2 Hz). Those are the definitions avail
able in the clinical neurophysiology literature (Remond,
1974). Although not exactly qualitative the definitions
contain a lot of empirical notions as "clearly distin
guished from background activity," "recognized form,"
"prevalently negative polarity," "amplitude generally
greater," "about 3 c/s." There are aspects where there are
no definitions, as the morphology of the spike and the
interval between the spike and the wave. There are aspects
open to the personal interpretation of the EEG scorer.


CHAPTER IV
SYSTEM EVALUATION AND
PRESENTATION OF RESULTS
Description of Data Collection
The data for the PM study was collected in the
Veterans Administration Hospital, Neurology Service, from
an ongoing drug study. At the time, Dr. B. J. Wilder was
evaluating the clinical efficacy and safety of valporic
acid (Depakene) in patients with uncontrolled absence sei
zures .
Twenty-five patients (14 men and 11 women) with
absence seizures were the subjects of the study. Almost
all the patients (23) were receiving other anticonvulsant
drugs. The central part of the study spanned a period of
4 months. One EEG tracing was obtained in the pre-entry
period; then a two-week single blind placebo period was
followed by the second EEG. Ten weeks of therapy with
valporic acid then followed. Another EEG tracing was
obtained at the end of this period.
The EEG's were for the most part obtained with a
4 channel telemetry system (Datel Model 1000, Physiological
Telemetry Systems), and the patients were free to move
about in a 3x5 meter room. There were different monopolar
montages used, but the ones most frequently utilized were
165


0
TABLE IV
COMPUTER/HUMAN AGREEMENT FOR INDIVIDUAL PATIENTS
PATIENT #3
Human
1 < Sz < 3 sec
3 < Sz
< 10 sec
Sz > 10
sec
Computer
Agreement in
Seizure Detection
(# of Sz)
399
221
74
90
31 ^
31
Agreement in
Seizure Duration
(# of Sz)
200
63
24
Total Time in
Agreement (sec)
416
. 421
514
576
Computer Counts
245
92
26
Computer Misses
178
16
0
Computer False
Detects
37
0
0
176


TABLE VIIcontinued
PATIENT #5
193


820 sec
Fig. 46. Variance Half Period Versus Half Period (#12-1)
222


289


143
Fig. 25. PM Detector Flow Chart. Dotted Line Mean Data
Dependent Path.


144
entry and output. To turn the communications between these
programs bimodal, they would have to be broken down further
without showing any relevant advantage, except possibly
easier testing. On the other hand, this would have
increased the computation time. Another characteristic
that is shown in the diagram is the dependence of the com
munications on the input data (dotted lines). For
instance, the closed loop in PEAK means that control is in
the module up to the point where a slow wave is detected.
A typical "closed loop" description on the algorithm
goes as follows: After initialization (MAIN) the program
analyzes serially the occurrence of a spike (SPIKE) and of
a slow wave (PEAK) in the filtered data (FILTER). The con
trol remains in PEAK up to the point where a slow wave is
detected. For every input point, the program also tests
for the occurrence of a spike. The communication between
SPIKE and PEAK depends on the particular phase of waveform
recognition. When three slow waves with the prescribed
repetition rate and at least one spike are detected, the
beginning of a seizure is acknowledge (MAIN); flags are set
at the output; and the time of occurrence is stored in
memory (SZURE). The program keeps looking at more slow
waves (PEAK) and spikes (SPIKE), storing the amplitude and
period for each event (STATIS). The periodicity of the
slow waves is checked (SZURE), and when no slow waves are
detected for the last 1 sec, seizure count is halted; sta
tistics of the detection parameters are obtained (STATIS)


72
Fig. 6. Additive Model for Quantization


19
in a sequence to produce the complex grapho-elements from
which, using superposition, the notion of pattern is
acquired. The variability in time and hemispheric location
gives rise to the time domain structure and topography of
the EEG. The job of the electroencephalographer is to
individualize these elements and compare them to his
acquired set of "normal activity" in order to make the
diagnosis. Of course, the boundaries are quite fuzzy,
highly subjective, and not always consistent (Woody, 1968;
Rose, 1973). .
The techniques are then dependent upon the specific
detection task desired, and no simple overview is possible
besides the translation to electronic terms of the decom
position process: analysis of the wave's amplitude in cer
tain frequency ranges, which implies broad bandpass filter
ing, zero crossing, and threshold analysis. Depending upon
the criteria formulated the next step can be the testing of
the grapho-elements throughout further processing (sharp
ness or repetition period, for instance) or testing of a
pattern by coincidence logic. What makes the process some
what erratic is that there is no methodology beyond the
extensive comparison with the results obtained by the
electroencephalographer and accordingly modify the imple
mentation or the criteria until an agreement is reached.
Due to the diversity of techniques, the detection of
abnormal brain activity (spikes) will be emphasized. One
of the first criteria to detect spikes was the sharpness


43
TABLE I
REQUIRED NUMBER OF ZEROS
t3
n
i*
Z = -1
Direct substitution
narrow-band
1
1
Direct substitution
wide-band
2
1
Bilinear
2
2


27
expensive. The inverse filtering can not differentiate
among types of nonstationarities. Therefore, a preproces
sing or other ancillary methodology needs to be developed.
Kalman filtering is quite sensitive to the gain setting.
For high gains small changes can be exaggerated, and so one
is faced with the problem of calibrating the filter, which
is usually done with a control data set (artificially gen
erated) The direct dependence of the gain on the type of
data, the dependence of the error signal on the power of
the input sequence, and some transient behavior of the
system are shortcomings.
It seems that the popularity of frequency domain tech
niques in EEG detection stems from the availability of
standard software packages and a fairly well developed (but
often forgotten) mathematical methodology. Up to the pre
sent, one of the drawbacks of the time domain approach is
the implementation medium (hardware) which requires a full
engineering development, not always accessible to the
clinicians. However, the present innovation trend in
microcomputer systems may very well bring the possibility
of standardization through the software implementation of
detectors, at low price.
To build an electronic detector where some parameters
(amplitude in a prescribed frequency range, zero crossing,
sharpness) have to be monitored and decisions made, the
omissions created by the poor quantization (definitions) of
the EEG process have to be filled. That is the reason why


287
TITL ST A TIS'
**** *** ******4e*** fc****^**.* *
* STATIS
$£:#* ifc*#:*:^*-*:* i*:* 5**-#*:*:$:***£*
* COMPUTES RUNNING AVERAGES.
* C3TAINS MEAN VALUES AND
* VARIANCES.
* MEAN R1
* VARIANCE R 4
* DATA IS FORMATTED TO USE
* ALWAYS MOST X OF 3 ITS.
CODE (REEFERS TO .MOST SIG. DIGIT)
* 0 TRUE MAGNITUDE
* 4 DATA SHIFT L. 1 HEX DIG.
$ 0 H 2 ti
* C ONLY VARIANCE SHIFT R. 1 HEX DIG.
REGISTERS USED
*
RO
INPUT DATA
*
R 1
MOST SIG. WORD OF MEAN

R2
LEAST * '
It It
R3
X OF ENTRIES
*
P 4
MOST SIG. WORD OF VARIANCE
*
R5
LEAST


P6
SCRATCH
2590
AORG >2590
FC 22
FLAG
EQU
>FC22
FC26
MASK 4
EQU
>FC26
FC2S
MASKS
EQU
>FC2S
2590
CS20
MOV
2FLAG,3FLA G TOTALS?
2 59 2
FC22
2594
FC22
2596
1600
JNE
FINI
2598
A080
A
0.2
NO,FORM PUNNING AVE.
2 59 A
1701
JMC
SMAL1
OF MEAN
2 59 C
0581
INC
1
DOUBLE PRECISION
2 59E
0 583
SMAL 1
INC
3
X OF ENTRIES
25A 0
C 180
MOV
0.6
GET X*X
25A2
3980
MPY
0,6
2 5A4
A1 06
A
6 .4
RUNNING AVE FOR VARIANCE
25A6
A l 47
A
7,5
25A3
1701
JNC
SMAL2
2 5A A
0584
INC
4
25 AC
0380
SMAL2
RTWP
*
£
TOTALS
25AE
3C43
FI N I
D I V
3,1
R1 HAS MEAN
2500
3 C 03
D I V
3,4
R4 HAS 1/N*SUM(X*X)
2 582
1910
JNO
SMALL
DIVISION POSSIBLE?


CHAPTER III
A MODEL FOR PETIT MAL SEIZURES
AND ITS IMPLEMENTATION
Detection Problem
The automated detection of pathological paroxysms in
the EEG is at the present time an unsolved problem. The
main reasons are the variability of the wave patterns and
the nonexistence of quantitative definitions of pathologi
cal paroxysms and of their elements (spikes and slow
waves). A paroxysm is a group of waves which appears and
disappears abruptly and which is clearly distinguished from
background activity. When the paroxysm is not related to
normal brain function, it is called pathological (epilepti
form) EEGers differentiate between interictal epileptic
discharges (events that are not accompanied by clinical
seizures) and ictal epileptic discharges (when clinical
seizures are evident). The definitions are in general hard
to apply, but for the special case of petit mal (PM) epi
lepsy the difference is solely based on the duration. It
was found that spike and wave bursts with duration shorter
than 3 seconds did not affect appreciably the behavior of
the patient (Sellden, 1971). Throughout this work the
evaluation of the detector will be restricted to the ictal
95


APPENDIX I
CHEBYSHEV FILTER DESIGN
Chebyshev Polynomials
The general formula for the Chebyshev polynomials of
order n is (Weinberg, 1962)
T (w) = cos (n arcos w)
(1-1)
n
which approximates a low pass characteristic with a magni
tude that does not exceed a prescribed maximum deviation in
the passband and displays the fastest possible rate of cut
off outside the passband (Fig.1-1). Equation (1) can be
transformed into a more recognizable polynomial form by
letting
, -1
(J) = cos w
and substituting again cos c|>=w and sin cj>=/ 1-w^, giving
T (w) = cos ncf> = R (cos+j sin n
n
(1-2)
+:
n(n-l) (n-2) (n-3)wn ^(1-w^)^
4!
O
Using trigonometric identities for cos ((n-1) ) and cos (n)
the following recursion relation can be derived
239


TABLE IVcontinued
PATIENT #4
Human
Computer
1 < Sz < 3 sec
3 < Sz < 10 sec
Sz > 10 sec
Agreement in
Seizure Detectior
(# of Sz)
221
121^\^^^
00 /
CN /
/ ^
/ ^
10
10
Agreement in
Seizure Duration
(# of Sz)
120
15
8
Total Time in
Agreement (sec)
116
93.7
225
152
Computer Counts
139
22
8
Computer Misses
10
6
0
Computer False
Detects
25
0
0
177


TABLE VII
PM STATISTICS FOR INDIVIDUAL PATIENTS
PATIENT #3
191


45
responses must "peak" up at the same place in frequency to
make any designs useful, and the response is repeated in
definitely at fs intervals (no matter what jw frequency
corresponds to fg/2). The answer must be found in the ele
ments that constitute the network in the Z domain and which
are dependent upon the transformation used. In the case of
the bilinear, there is always at least one zero mapped at
z=-l, which sets at this point the amplitude of the fre
quency response at zero. So the zero is responsible for the
good attenuation properties of the bilinear transform near
the folding frequency. This observation is worth noting
since it will be useful in the design using nonrational
mappings.
The best known nonrational transformation is the impul
sive invariant (Oppenheim & Shafer, 1975). There are a few
slight modifications, and the direct substitution method
will be employed here (Childers & Durling, 1975), where
(s-a.) -* (z-eaiT). (7)
i
are the S plane filter poles. Due to the periodicity of
the exponential function, the transformation is not one to
one. The net effect is that each strip of width w in the
O
S plane will be overlayed onto the unit circle; i.e., the
points w^+Kws (K=l,2,...) will all be mapped into the same
point as w^. Mathematically, the frequency response of the
digital filter H(e-^w) is related to the frequency response
of the analog filter (Oppenheim & Shafer, 1975) as


60
Fig. 3a. Overflow Characteristics of Two's Complement
Fig. 3b. No Overflow Propagation Region


Fig. 5c. 4th Order Filter.
~4
o
Feedforward Implementation (Wide Design).


99
waned and was maximal at the onset of the paroxism.
Finally the wave was of high amplitude (150-200 yV) maximal
in the frontals, and with duration 200-500 ms. If the pos
itive transient is considered separately, the duration of
the negative wave is 150-200 ms. It is worth pointing out
that the limits for the period parameters of the various
components leave room for an harmonic frequency relation
among them; i.e., taking the period of the slow wave as the
fundamental frequency, the positive transient appears at
2 f_TT, spike 2 at 3 f_TT.
sw c sw
A Petit Mai Seizure Model
The detection of PM epochs can be divided into two
parts: the detection of the individual components and the
definition of the pattern recognition scheme. The weight
of the detection elements in the overall scheme will follow
the constancy of the paroxysmal elements in the real data.
The most reliable element in the PM pattern is the slow
wave component since the spike may be absent or substituted
by polyspikes. The amplitude information of the waves is
also widely dependent from person to person (as the EEG
amplitude is) and is also sensitive to the electrode place
ment. Therefore, it was thought that the most reliable
parameter is not the amplitude of the elements but their
frequency information. Another parameter which will be
used for the first time is the measure of the repetition
rate of the wave complexes (the PM recruiting rate).


257
When the coefficient is involved in the computation, an
alignment operation must be performed. However, an advan
tage of storing the coefficients less than one in full pre
cision was discovered: the result of the multiplications
are automatically scaled when the 16 less significant bits
of the result are dropped. This point needs a detailed
analysis. In a multiplication with a number less than one,
the result is at most of the same magnitude as the input.
To preserve the real magnitude of the input, and as the
coefficients are stored as integers, the result of the
multiplications need to be scaled down. But storing the
coefficients full precision when they are less than one
means that a shift left of 16 was performed in their
values. When the lower order word of the product, which
contains the least significant bits is dropped (to keep the
computation wordlength constant), a shift right of 16 is
actually performed. Hence, the least significant bit of
the part of the product retained becomes automatically
aligned with the input, no matter where its binary point
might be. As there are at least as many coefficients less
than one as greater than one, most of the times the scheme
implemented does not require alignment.
The alignment of the product involving the coefficient
greater than one is readily done if it is kept in mind that
the relative weight of the coefficients shall be maintained.
This operation increased the computation time signifi
cantly, and so it was decided to perform a shift left of


CHAN 1 Input EEG
CHAN 2 Slow Wave Filter
CHAN 3 Detections
150
1sec.
Fig. 27a. PM Detector Output (Patient #7)
154


25
filters (22-45 Hz spike, and 1.5-4 Hz slow wave), followed
by threshold logic to input the basic elements to the
microcomputer memory, where the pattern recognition takes
place. The system had no false detects in selected epochs,
but was very sensitive to irregularities of the pattern in
the middle of the ictal event.
Selection of the Method of Seizure Detection
The requirements put on the analysis method related to
the specific problem of detection of paroxismal events are
the following:
1) The detection shall be performed in real time in
one channel, using a microcomputer.
2) The detector shall have high resolution capabili
ties and be insensitive to high energy artifacts.
3) It shall also be able to quantify in detail the
paroxisms.
The computation time constraint is probably enough to
make the selected choice of analysis obvious, since FFT
algorithms that run real time in simple microcomputers,
with workable resolutions, are not known to exist. But
even in the affirmative case, it seems that spectral analy
sis is not tailored to event detection in the EEG because
the spectrum produces a smoothing (leakage/resolution). To
compensate for it, longer sequences and/or special tech
niques (parametric spectral analysis) need to be used,
which increase the computation time.


145
along with the duration of the event. The program returns
to main (MAIN) to flag the output and restart the loop.
MAIN, PEAK, and SZURE use the same workspace and are
linked through a branch and link (BL) instruction. SPIKE
uses an independent workspace linked through a branch and
link workspace (BLWP). Each filter uses 2 workspaces
(BLWP), and for the statistics of each parameter another
workspace is utilized (BLWP). The interrupt handler uti
lizes the workspace assigned to the interrupt level III.
Fig. 26 presents the memory mapping of the final program
and constants definition. It occupies RAM memory from
2000 to 2700, and the workspaces are placed in the top of
£1
memory, from FCE2 to FE40tI. External references are placed
£1
at FC00 to FC2E .
H
Description of the Programs
A brief description of the program is going to be
presented in this section. The programs are entirely writ
ten in TI assembly language, are well commented and are
presented in Appendix III. To develop the programs a
crossassembler from a NOVA 2-10 computer to the TI language
was used along with the TMS 9900 assembler resident in the
AMDAHL 470 V6.
MAIN. Besides performing all the initializations,
MAIN also tests the repetition rate of the slow waves
detected. Rl is used as the repetition rate counter. The
periods in the hexadecimal are 34H, 80^. After detecting


262
0169
0094
21B4 09C8
SRL
8,12
0170
0095
21B6 E1C8
SOC
8,7
0171
0096
21B8 A1C9
P0ST5
A
9,7 C(X1+E)-DX2+E IN R7
0172
0097
21BA 0003
MOV
3,0 XFER YN TO 2ND RESONATOR
0173
0098
*
0174
0099

CALCULATION OF 2ND RESONATOR
0175
0100

RECURSION RELATION IS
0176
0101
i
X1+=-DX2+E+C(X1-£)
0177
0102
ft
X2X1-E
0178
0103
ft
Y=X2
0179
0104
ft
REG USED
0180
0105
*
R16 FOR E
0181
0106
ft
R7 FOR
X1
0182
0107

R3 FOR X2
0183
0108
ft
0184
0109
21BC 02EC
LWPI
FIRST
0185
21BE 2CE2
0186
0110
21C0 0743
Tbs
3
0187
0111
21C2 38C2
MPY
2,3
0188
0112
21C4 1101
JLT
POST 3
0139
0113
21C6 0503
MEG
3
0190
0114
21C8 AOCF
POST 3
A
15,3
01 <51
0115
21CA C243
MOV
3,9
0192
0116
21CC 61CF
S
15,7
0193
0117
21CE C0C7
MOV
7,3
0194
0118
2IDO 0747
AB3
7
0195
0119
21D2 39C1
MPY
1,7
0196
0120
21D4 1501
JOT
POST 4
0197
0121
21D6 0507
NEG
7
0198
0122
21D8 A1C9
P0ST4
A
9,7
0199
0123
21DA 0843
MOV
3*13
0200
0124
ft
C2C1
0125
ft
ENO OF FILTER CALCULATIONS
0202
0126
C2C3
0127
21DC 1CFF
JMP
$
0204
0128
21DE 1CCC
NOP
0205
0129
21EC 1CD2
JMP
BACK
C2C6 013C END
' 0207 *0000 MO.Cc ERRORS IN THIS ASSEMBLY= COCO
0208 NO. CF RELOCATABLE LOCATIONS USED = OCOO
0209 9 OF OBJECT RECORDS CUTHJTs 9
0210 END CF ASSEMBLY
PROCEED


3.47 sec
R. Period Versus Duration (#5-1)
Fig. 40a.
209


Petit-Mal Seizure Detector and Analyzer
Fig. 24. PM Detector Functional Diagram
141


17
To cope with the EEG nonstationarities, recently there
have been reports on Kalman-filtering (Isaksson & Wennberg,
1976). If the stationarity constraints are removed from
the noise in the ARMA model, it can be shown that the best
fit in the least mean squared sense to the time series is
achieved by the Kalman filter (Kalman, 1960; Isaksson,
1975). So, this filter is a generalization of the Wiener
filter for nonstationary data and is closely related to
autoregressive techniques. It consists basically of the
ARMA fit to the time series, but due to the inclusion of a
feedback loop with variable gain (Kalman gain) the locations
of the poles of the system are allowed to vary. The key
parameter in the design is the setting of the Kalman gain
since it weighs the new value of the residual signal with
its past values and changes accordingly the coefficients of
the all-pole filter. The gain controls then the adapta
bility of the filter. If the gain is set at zero, the
Kalman filter is just an ARMA fit for the incoming data and
is nonadaptable. If the gain is increased, then we have
adaptable properties and the tracking is improved with the
gain. One important consequence of the adaptability of the
filter is to avoid the smoothing effect present in other
spectral methods. Incidentally, by comparing the autocor
relation function obtained by any of the stationary spec
tral methods with the autocorrelation function estimated
from the output of the Kalman filter, some knowledge about
the limits of the record length to preserve stationarity


30 Hz
Input 0.1 volts (10 V P.P.)
Fs=80 Hz. Linear scales.
Fig. 15a. Slow Wave Bandpass Frequency Response
121




122


57
ROUNDING
Q(x)
TRUNCATION
A=2 where b+1 is register
length.
Fig. 2. Quantization Error


15
stored in the computer memory. For EEG, prewhitening is a
must, since the background activity (noise, if a particular
pattern has to be detected) is not white. Matched filter
ing has been used for spike detection in EEG by Saltzberg
(1972), Zetterberg (1973), and more recently by Barlow and
Sokolov (1975) and Eftang (1975).
Another result borrowed from communication theory is
inverse filtering. The inverse filter is generally applied
to extract information about the arrival times of the indi
vidual components of a composite waveform (Childers & Dur-
ling, 1975; Robinson, 1967). It is required to know the
shape of the waveform and to make the stationarity assump
tion on the background noise. The filter is nonrealizable
(the output is theoretically a delta function), and great
care must be taken in the required inversion of the Fourier
transform of the waveform not to divide by zero. Inverse
filtering also deteriorates the S/N ratio, and a compromise
has to be reached between resolution and signal-to-noise
ratio.
In EEG inverse filtering is used in a different way.
Barlow and Dubinsky (1976) use inverse filtering to gener
ate the impulse responses of bandreject filters (EEG > power
spectrum -> square root individualize band of interest -*
subtract from uniform spectrum (with amplitude equal to
maximum) -* IDFT (to get impulse response) ) This procedure
is highly sensitive to truncation effects, and so poor fil
ters result. Lopes da Silva et al. (1975) use a linear


TABLE IVcontinued
PATIENT #7
Human
Computer
1 < Sz < 3 sec
3 < Sz < 10 sec
Sz > 10 sec
Agreement in
Seizure Detection
(# of Sz)
70
32
14
14
26
26
Agreement in
Seizure Duration
(# of Sz)
32
12
26
Total Time in
Agreement (sec)

76
84
443.2
361
Computer Counts
64
20
26
Computer Misses
38
0
0
Computer False
Detects
32
6
0
179


31
present been implemented in analog form. The remainder of
the pattern recognition algorithm is implemented digitally.
Analog filters have the disadvantage of being very sensi
tive to changes of the component values produced by envi
ronment parameters like temperature, humidity, and aging.
Although there are design methods that can minimize the
sensitivity to component changes (e.g., leap frog), they
are more difficult to design since in such structures there
is a~ substantial:number of feedback loops and the change of
one filter parameter implies the modification of a large
number of filter components. Another problem to which
analog filters are sensitive is the tolerance in component
values. To design two filters with identical character
istics some or all of the components have to be hand
matched. However, this procedure only applies to that
particular point in time, since the matched components can
have different aging coefficients and so evolve differently
in the long run.
The identical filter characteristics are stressed here
because, at the present time, a sensitivity analysis which
can be applied to the detection of EEG waveforms is not
available. However, it is known from experience that very
small differences in the filter parameters and/or pattern
criteria produce drastic changes in the detection (Smith,
1979). Therefore, the only way similar detection charac
teristics can be guaranteed between two systems is to match
every detection stage.


40
high as 5 Hz) since the spike principal component can be as
low as 11 Hz, roughly one octave away. Otherwise, the
spike energy will degrade the periodic appearance of the
slow wave filter output, preventing the use of full cycle
detection, which has been considered the best (Smith,
1978).
After this quick analysis it can be said that the
overwhelming filter characteristics are the good out-of-
band attenuation and the low Q. The Q is a factor con
trolled by the filter parameters and not by the filter
type. Therefore, a "good" EEG filter shall display fast
out-of-band attenuation. With this constraint in mind, the
filter type chosen will be the Chebyshev, since it displays
the optimum out-of-band attenuation rate for a certain
order, when all the zeros are assumed at infinity (Wein
berg, 1962). Elliptic filters have similar attenuation
characteristics but are more difficult to design due to the
proximity of the poles and zeros. Also for a digital fil
ter implementation this fact means complex zeros and subse
quently more multiplications.
To design the digital filters and use the present
experience with analog filters it was decided to accomplish
the design in the S plane and use one of the mapping rules
to the Z domain (impulse invariant or bilinear). It was
thought important to have an automated facility to design
the filters from the frequency domain filter characteris
tics, i.e., center frequency, bandwidth, ripple in-band and


109
detector uses the digital representation instead of the
analog signals, much more resolution is needed. As an
example, consider that the period measurement of one sine
wave of 16 Hz is desired with a precision of 0.25 Hz.
Theoretically, a sampling frequency of 80 Hz would be more
than enough to represent the sine wave. However, its fre
quency, using zero crossings, can only be known, from the
digital representation, with a precision of 3.2 Hz, accord
ing to the expression (Smith, 1979)
fg = f2/Af.
(48)
This clearly points out that the parameter extraction must
be accomplished with more sophisticated techniques (for
instance, interpolation) or that much higher sampling fre
quencies must be utilized.
The determination of the zero crossing using the
linear interpolation between points and assuming sinusoidal
activity was worked out.
t=0
S2
Fig. 12


308


CHAN 3 Input EEG (Szf #7)
CHAN 4 Spike Filter Output
CHAN 5 Spike Detector Output
CHAN 6 Input EEG (Muscle)
CHAN 7 Spike Filter Output
CHAN 8 Spike Detector Output
1 sec
Fig. 19. Spike Detector Performance
150 yV


314
2422
C 801
MOV
1 S> MASK2
2424
FC32
2426
0202
LI
2 Q R IGN
2423
2720
242 A
0203
LI
3 .KEY
242C
FFFF
242E
02 04
LI
4 >F
2430
0 0 OF
2432
0207
LI
7,WSTA1
WSP FOR MEAN
2434
FD 80
2436
0208
LI
8,ST ATI
24 38
2580
2 43 A
0209
LI
9.WSTA2
MSP FOR VARIANCE
2 43 C
FO AO
2'4.3E
0 2 OA
LI
10,STAT2
2440
2580
2442
Cl 82
GACK
MOV
2,6
2 444
8002
C
2,0
LAST POINT
2446
1349
JEQ
OUT
2 44 8
0226
AI
6,4
2 44 A
0004
244C
80 06
C
*6,3
SMALL SZ?
244E
1603
JNE
GIG
2450
C 2 22
A I
2.6
GET NEXT FFFF
2452
0006
2454
1 OF 6
JMP
SACK
2456
Cl 32
GIG
MOV
2,6
245 8
A1 AO
A
3AD0X,6
GET POINTER TO MFM
245A
PC 00
245C
8120
C
SAODX,4
AMPLITUDE?
245E
FCOO
2460
1 323
JGT
AMP
2462
Co 16
MOV
*6, 12
R12 GETS DATA
2464
432 0
SZC
3MASK1 ,12
2466
FC30
246 8
0 28C
Cl
12,0
REAL MAG*?
2 46A
0 0 00
246C
132E
JEQ
CONT
246E
02 SC
Cl
12,>4000
4 IN M S B ?
2470
4000
2472
1 3 OD
JEQ
FOUR
2474
45A0
SZC
3MASK2,*6
M.S.3 IS 3
2476
FC32
2478
C316
MOV
46,12
247A
oaac
SPA
12 ,8
SHR MEAN 8
247 C
04 07
8LWP
7
FORM RUNNING AVE.
247E
C58C
MOV
12, *6
2430
0 5C6
I NC T
6
2482
C206
MOV
*6, 1 1
2404
0 338
SPA
11 .8
SHR VAR 8
2 48 6
Co 48
MOV
11,49
2488
C588
MOV
11,46
2 48A
0409
BLWP
9
FORM RUNNING AVER.
248 C
1023
JMP
TEST


237




14
method of Gotman and Gloor (1973) consists of a spatial
arrangement of polygons of different sizes related to
the ratio of (delta + delta)/(alpha + beta) which is
thought to be a good descriptor of localized brain abnor
malities. It is considered to be a good descriptor for
detection of slow wave abnormalities and asymmetries in the
EEG if a preprocessing for gross artifacts in the raw data
is performed.
The results of optimum filtering have also been applied
to extract certain features from the EEG. One of the ear
liest techniques was matched filtering (Smith et al., 1969;
Zetterberg, 1973; Saltzberg, 1971). A matched filter is
the filter that maximizes the signal-to-noise ratio, since
it transforms all the available information (energy) of the
input signal in a voltage at a specific time x. The pre
requisites for its construction or modeling are the a priori
knowledge of the waveform shape and the stationarity of the
background noise. A matched filter is in fact a correla
tion detector, and a relatively simple way of implementing
digitally one (for a white Gaussian noise) is to select a
wave pattern, store it backwards in memory, and perform a
correlation with the input (template matching). If the
noise is not white, we have to prewhiten it and separate
the implementation into two steps: first, divide the
Fourier transform of the desired wave pattern by the power
spectrum of the noise and second, inverse transform the
resultant spectrum to obtain the template that can be


73
error. It is common to make the following assumptions on
the additive noise process (Gold & Rader, 1969):
1. The sequence of error samples e(n) is a sample
sequence of a stationary random process.
2. The error sequence is uncorrelated with the
sequence of exact samples x(n).
3. The random variables of the error process are
uncorrelated; i.e., the error is a white noise
process.
4. The probability distribution of the error process
is uniform over the range of quantization error.
It is worth pointing out that the above-mentioned
hypotheses are approximations that do fail for special
types of signals, the most important being the class of
constant inputs. But when the sequence x(n) is a complex
signal and the quantization step is small, it gives good
results. Therefore, the model presented in Fig. 6 will be
used for most of the quantization effects in the filter
implementation.
The assumption that the error is signal independent is
a good approximation for rounding, but for truncation it is
clearly not true, since the sign of the error is always
opposite to the sign of the signal (20). However, it is
easily shown (Oppenheim & Shafer, 1975) that this effect
can be incorporated in the mean of the noise process. For
2
truncation, the mean value m_ and the variance a are
e e
given by


SAVE PREVIOUS VALUE
2 546
COCO
MOV
0.3
2 54 S
Cl 66
MOV
3>E(6),5
2 54A
COOE
2 54 C
OOCQ
C
0 -j
254E
l 5F9
JGT
POSTV
2550
A 203
A
3,3
2552
0587
INC
7
2554
16EB
JNE
NEXT
2556
0868
SR A
8,6
2553
1000
MOP
2 55A
0204
LI
4 ,GAINW
255 C
00 11
2S5E
3908
MPY
8,4
2560
0845
SRA
5,4
2562
0204
LI
4, 3
2564
0003
2566
3 944
MPY
4,5
2563
C806
MOV
6.3THRES
2 56 A
FC04
256C
0204
LI
4,GAINS
256E
00 13
2570
39C8
MPY
8 .4
2572
0845
SRA
5,4
2574
0204
LI
4, 3
2 57 6
0 003
2573
3944
MPY
4,5
2 57 A
C806
MOV
6,3SPTHR
257C
FC02
END
NO CF ERRORS IN TH IS ASSEMOLY= 0000
RELOCATABLE LOCATIONS USED = 0000
ADD WITH PREVIOUS
LAST POINT?
DI V BY 54
S.W. FILTER GAIN
SCALE BY GAIN
GET 75 UV
STORE VALUE
SPIKE FILTER GAIN
SPIKE THRES


46
(8)
Ha(s) is the Laplace transform of the filter impulse
response and T the sampling interval. It is clear that
only if H(w) is bandlimited to ws/2, (8) will be a reason
able description. This fact excludes the use of the direct
substitution to design high pass filters and in general any
function which will display appreciable energy at half the
sampling frequency. Anyway it can be expected that the
attenuation characteristics of the high frequency end of
the filters designed with the straight direct substitution
method will be worse than if the bilinear was employed.
For the case of bandpass filters, the zeros of the S plane
transfer function, if not at s=, can fold back in the
bandpass, ruining the design. Therefore, it is a good
design procedure not to map the zeros of the s plane trans
fer function using this transformation.
It was decided to place the zeros independently in the
Z domain. As the filter is a bandpass, at least one zero
must be placed at z=l to block the d.c. gain. Taking into
consideration the preceding discussion of the effect of the
zero at z=-l, it was decided to place the other zero(s) of
the transfer function at z=-l to obtain the good attenua
tion characteristics of the bilinear transform. The other
convenient properties of the zeros at z=l are the


221


258
3 bits in the filter coefficient greater than one before
storing it. The coefficient was then stored as B140H
for our previous example. There is then only one bit dif
ference in the relative magnitude of the coefficients;
therefore, a shift left of one in the part of the product
retained needs to be performed. For one bit it was decided
to leave the least significant bit zero, and so a consider
able savings in the computation time was accomplished.
It is worth recognizing that this scheme does not lead
to overflow, as long as the input is correctly represented,
for two reasons: First, the overflow analysis takes the
increase in wordlength, due to the multiplications, into
consideration. On the other hand, the multiplication is
unsigned, and the product is correctly aligned with the
input. As said earlier, the multiplication is unsigned,
so the programmer needs to take care of the sign of the
product. As in this case the sign of one of the operands
is always known (the filter coefficient), it is necessary
to extract only the information of the sign of the input.
This was accomplished by taking the absolute value of the
input (making it always a positive number) and then
negating the result of the product if the input was nega
tive and the coefficient positive (or vice versa).
The filter algorithm is less than 40 instructions long
and was measured to take less than 300 ys to execute. To
measure the computation time, the output of the D/A was
monitored with a scope and the numbers which control the


147
CONSTANTS
FCOO
DELAY
FC02
SPTHR
FC04
THRES
FC06
MASK
FC08
PCI
FCOA
PC2
FCOC
PC3
FCOE
STATl
FC12
STAT2
FC16
STAT3
FClA
STAT4
FC1E
STAT5
FC22
FLAG
FC24
SZT1M
FC26
MASK4
FC28
MASK8
FC2A
LESS3
FC2C
LES10
FC2E
GRT10
Fig. 26continued


56
performing the additions. If two fixed point numbers are
added, overflow can occur (Gold & Rader, 1969), and as
there is a linear relation between dynamic range and word-
length, the probability of overflow is large. For the
fixed point multiplication, overflow can never occur.
However, quantization of the true value shall be generally
made, since the product of two b-bits numbers is two
b-bits long and it is general practice to use a constant
wordlength throughout the filter calculations. For float
ing point representation a positive number F is represented
by F=2CM, where M, the mantissa, is a fraction, and c, the
characteristic, can be either positive or negative.
Quantization of the mantissa is necessary for both the
addition and multiplication. Overflow is also theoreti
cally possible, but as there is an exponential relation
between wordlength and dynamic range, it can be essentially
excluded. It is therefore assumed that floating point is
overflow free.
Truncation and rounding are the two forms of quantiza
tion. The quantization error is defined by
£ = x-Q(x) (18)
where Q(x) is the portion of x, the input signal, retained.
The quantization error depends upon the type of number
representation used as shown in Fig. 2. In a microcomputer
implementation, the two's complement is the natural choice
because it is employed in the processor's arithmetic unit.


PLOT VERTI STEP
2282
2264
A12A
00 10
A
£>l0(10),4
2238
2288
C66A
0002
PL 2 V
MOV
22( 10) 4c9
223A
228C
223 E
CA6A
0004
0002
MQV
34(10),32(9)
2290
069C
BL
*12
2292
2294
812A
0004
C
34{101.4
2298
1503
JGT
NEG
229 3
229 A
0 5AA
0 0 04
INC
34(10)
229C
1002
JMP
CONT
229E
2 2 AO
062A
0004
NEG
DEC
-34 ( 1 0)
2 2A2
2 2 A 4
S12 A
0004
CO NT
C
24(10) ,4
22A6
22A 8
1 6EF
0380
JNE
RTWP
FLOV
4c
POSIT STEP?
4e
*
INTERPOLATION
22AA
CA34 LINE
MOV
4.36(10)
22AC
0006
2 2AE
C 102
MOV
2,4
22B0
39 l A
MPY
*10 ,4
2 23 2
3D 03
DI V
3 ,4
2234
A1 2 A
A
£ > 10(10)
223 6
0010
2 23 8
CA 84
.MOV
4,aa(io)
22BA
0 0 03
223C
CA AA
MOV
36(10).3
22BE
0006
22C0
C 0 0 A
22C2
6AAA
S
32(10 ) ,3
2 2C4
0002
2 2C6
000 A
22C3
076A
ABS
3>A(10 )
22C A
000 A
22CC
02 C
STST
6
22CE
CA AA
MOV
34(10) ,3
22DC
0004
22D2
OOOC
2 2D 4
6A34
S
4,3>C(10
22D6
OCOC
2 2D 8
C76A
A3S
3>C ( 10 )
2 2D A
OOOC
2 2DC
124B
JEQ
FLAT
2 2D E
02CT
STST
7
22E0
SA AA
C
3>C( 10) ,
2 2E2
OOOC
2 2E4
OOOA
2 2E6
15 23
JGT
YBI G
NEW VALUE OF X IN NE'WX
GET NEW Y
NEW VALUE OF Y IN NEYiY
GET ASS OF DELTA X
STORE SIGN
GET DELTA Y
IF DELTA Y=0 JUMP
DEL TA Y>DELT A X?


CHAPTER II
MICROCOMPUTER BASED DIGITAL FILTER DESIGN
The purpose of this -chapter is to analyze the trade
offs in digital filter implementation using microcomputers
and arrive at a comprehensive design procedure. The design
approach proceeds from the study of the digital filter
noise factor to the choice of a microcomputer wordlength
and A/D converter precision, so that a specified output
signal to noise ratio could be obtained. This approach is
quite general and may be valuable even if future technolo
gies will make practical other implementation media (e.g.,
bit slice microcomputers).
Preliminary Considerations
For quite some time the EEG research group at the
University of Florida has been developing nonlinear methods
for the detection of EEG waveforms. Basically the detec
tors include bandpass filters followed by zero crossing and
threshold analysis of the filtered data to extract informa
tion about period, amplitude and number of in-band waves in
the raw EEG. The superiority of this detection method for
EEG activity has been established when the variability of
the patterns is fairly high (greater than 10 percent
Smith, 1978). The bandpass filters have up to the
30


sec
VO
1
1 hour
Fig. 33b. Sz Duration Versus Time (#5-2)
201


283
TITL SPIKE'
*$* *:jc £****** 44c **
* SPIKE
4*44 44444444444444444
* CHECKS PERIOD AND AMPL.
* OF TE SPIKE FILTERED DATA,
4 PASSES TO STATIS THE SPIKE
* AMPL. AND SPIKES.DELAY
REGISTERS USED
*
RO
SIGN GF INPUT

R l
SPIKE DURATION
*
R2
SPIKE AMPLITUDE
*
R4 ,
5 SCRATCH

R6
POINTER TO MAIN
2 49 0
AORG >2490
FD60
PIKE
EQU
>FD60
FC 02
SPTHR
EQU
>FC0 2
009E
COUNT
EQU
>9E
FCOO
DELAY
EQJ
>FC0 0
F C 06
MASK
EQU
>Fcoe
Foeo
MAIN
EQU
>FD80
FC 08
PCI
EQU
>FC08
FCOA
PC 2
EQU
>FC OA
FCOC
PC3
EQU
>FCO C
FC 16
STATE
EQU
>F C 1 6
FC1E
ST AT 5
EQU
>FC1E
FDEO
**STA3
EQU
> FDEO
FE 20
STA 5
EQU
>FE20
C 0 0 A
HP. A T E
EQU
> A
0 0 05
LRATE
EQU
5
2 49 0
02E0
LWPI PIKE
2492
FD60
2 49 4
0206
LI
6,MAIN
2 49 6
FDSO
2498
02 07
LI
U.
A
N
249A
0 0 OF
2 49 C
Cl 00
SACK
MOV 0,4
249E
CO 03
MOV 3,0
2 4A 0
4020
3ZC SMASK.O
24A2
FC06
24A4
C9A0
MOV
DPC1,5C(6)
24A6
FC 08
2 4 A8
OOOC
2 4A A
0380
RTViP
2 4 A C
8 100
C
0,4
24AE
13F5
JEC 3ACK
2430
04E0
CLR
£>1EF2
2432
1 EF2
2484
0280
Cl
0,>8000
SAVE SIGN OF INPUT
GET SIGN CF NEW POINT
LOAD PC FOR NEXT JUMP
CHANGE IN SIGN?
LAST POINT NEG?


286


TABLE VIIcontinued
PATIENT #4
192


34
signal. Here we will not discuss the validity of the
hypothesis but will acknowledge the fact that the signal1s
digital representation is an approximation. To describe
sampled waveforms in the time domain a sampling frequency
higher than the Nyquist rate should be utilized. There
fore, for real time processing a sampling frequency between
200 and 300 Hz seems adequate for most applications (Smith,
1979), which means, in the worst case, that the computation
time per sample must be less than 3.34 ms. An analysis of
the clock frequencies and the instruction cycles of today's
microcomputers shows that hundreds of operations can be
performed in this interval. It seems a comfortable margin
when one compares this number with the apparent simplicity
of the recursion algorithma few multiplications and addi
tions. "Apparent" is stressed because we are generally .
led to think in "terms of floating point arithmetic. It is
a good exercise to estimate the enormous number of opera
tions needed to perform a floating point operation when
using numbers greater than one as sole representations.
It turns out that the computation time becomes prohibitive
if floating point is utilized. There are other types of
arithmetic, like the block floating point (Oppenheim,
1970), which do not seem to bring any advantage for our
application.
The most severe limitation in the use of fixed point
arithmetic is the small dynamic range, since the maximum
1-
representable number is 2 where b+1 is the number of bits


APPENDIX II
DIGITAL FILTER IMPLEMENTATION
Preliminary Considerations
The Texas Instruments TI 9900 microprocessor was
selected for the implementation since it was one of the
only 16 bit microcomputers available at the time. It pos
sesses some interesting features for arithmetic signal
processing like multiply and divide instructions and an
architecture which is unlike most of the processors in the
market: The CPU only has three registers, the program
counter (PC), the workspace pointer (WSP) and the status
register (ST). The sixteen working registers are anywhere
in RAM memory in a block identified by WSP. Although the
memory architecture uses more memory and increases the
overhead for register to register operation (when compared
to the architecture of in-chip registers), it is very con
venient for context switches, because the machine's previous
state does not need to be saved. It is sufficient to
modify the contents of the WSP register.
This feature was thought very convenient for the
implementation of digital filters because it gave modular
ity to the programone workspace was allocated to each
second order resonator. Although the program was not
250


32
The substitution of the analog filters by digital ones
is also a natural extension of the present instrumentation
since the other functions of the pattern recognition algo
rithm are already digitally implemented. The repeatibility
and uniformity of characteristics will be therefore
ensured.
The implementation of digital filters could be accom
plished basically in two different ways: building special
purpose machines to implement the filter algorithm (hard
ware) or making use of general purpose computers and writing
adequate software to accomplish the filtering function.
The two techniques possess different properties that are
worth comparing. The main advantage of the hardware reali
zation is speed since the processor's architecture is in
tentionally adapted to the special type of processing, e.g.,
multiplications and additions (Gold et al., 1971; de Mori
et al., 1975). Generally, the processor is microprogrammed
and the arithmetic unit is implemented in fast ECL logic.
There are some minor modifications to the basic procedure,
the use of Read Only Memories to implement the multipliers
being the most interesting (Peled & Liu, 1974). However,
the development of a special processor is very expensive
and implies the availability of specialized laboratories
and the work of a diversified group of researchers.
On the other hand, the software implementation of
digital filters can be performed by anyone who masters a
computer language as long as the recursion relation is


22
possible to choose between the display of half or full
waves and have a better qualitative view of the rising and
falling phase of spike and wave activity. At this time,
however, the system is only qualitative (Harner, 1973)
since the definition of boundaries for spikes or spike and
wave complexes need medium computers and more resolving
power. One important theoretical defect of amplitude-
duration techniques, still not solved, concerns the mixing
of two frequencies having similar amplitudes.
Pattern recognition was also applied to the detection
of paroxysmal events in EEG (Serafini, 1973; Viglioni,
1974). The theoretical method for the determination of the
relevant parameters by performing data reduction (linear
principal component analysis (Larsen, 1969) and nonlinear
homeomorphic procedures (Shepard, 1966)) have hardly been
applied to the EEG (Gevins et al., 1975). The parameters
chosen are once again few in number and related to visual
analysis: amplitude and the average value of the waves,
number of zero crossings and mean value of zero crossings.
The experimental results show that the criteria are satis
factory, but it requires a training set, is critically de
pendent upon the length of the normalization interval, and
requires a fairly large number of decomposition (orthonor
mal) functions. Following the same line of pattern recogni
tion Matejcek and Schenk (1974), Remond and Renault (1972),
and Schenk (1974, 1976) applied a vectorial iteration tech
nique to decompose the EEG. First, the maxima and minima


02 sec
Fig. 42a. Half Period Versus Duration (#12-1)
215


315
248E
45 AO
FOUR
szc
2MASK2
2490
FC32
2492
C316
MOV
*6. 12
2494
0 84C
SR A
12,4
2496
0407
3LWP
7
249 8
C58C
MOV
12, *6
2 49 A
05C6
INCT
6
249 C
C2D6
MOV
*6,11
249t
0843
SR A
11 ,4
24A 0
C 643
MOV
1 1 ,49
24A2
C583
MOV
11 *6
24A4
0409
SLWP
9
24A6
1016
JMP
TEST
2A8
C316
AMP
MOV
46, 12
24AA
4320
SZC
3MASK1
2 4AC
FC30
24AE
02 3C
Cl
12 ,>C0<
243 0
COOO
2482
1309
JEQ
CONT3
24S4
C3I6
MOV
*6,12
243 6
0407
SLWP
7
2438
05C6
INCT
6
243 A
C2D6
MOV
46,11
243C
0 348
3RA
11,4
248E
C583
MOV
11,46
2 4C0
C54B
MOV
11 ,49
24C2
0409
OLWP
9
24C 4
1007
JMP
TEST
24C6
4 SAO
C0NT3
SZC
3MASK2
24C8
FC32
2 4C A
C3 1 6-
CD NT
MC V
46,12
24CC
0407
BL WP
7
2 4CE
05 C6
INCT
6
240 G
C556
MOV
46 ,49
2402
04 09
3LWP
9
2404
0222
TEST
AI
2, >1A
24D6
00 1A
2403
10 34
JMP
SACK
240 A
05A0
GUT
INC
3FLAG
2 40 C
F C 22
24DE
0407
2LWP
7
245 C
0409
3LWP
o
2 4 E2
0460
R
3MQNIT
24E4
0080
END
SHR 4- BITS
SHR 4- BITS VAR.
PUNNING AVER. FOR VAR,
C IN M.S.Z3?
SHR VARI .
CLEAR .MEAN OF C
GET REDDY FOR TOTALS
NC.CF ERRORS IN THIS ASSEMBLY^ G000
RELOCATABLE LOCATIONS USED = 0000


293
2 62 E
263 0
2632
064D
i 5FD
C3A0
DECT
JGT
MOV
13
LOOP
S3ZT1M,14
R1 4 GETS MEMORY POINTER
2634
2636
FC24
CF A 0
MOV
2TIME.* 14+
SEC COUNT IS LOADED IN MEM
2638
2 63A
FF9C
C360
MOV
STHRES,13
AMP THRES IS STORED IN R15
2 63 C
263 E
2640
FC 04
C3CD
0 A2D
MOV
SLA
13, 15
13,2
GET 3/4 OF THRES
2 64 2
2644
2646
2643
264A
2 64C
63 4 F
092D
CSOD
FC04
04C1
0 2 OD
S
SRL
MOV
CLR
LI
15, 13
13,2
13,8 TH RES
1
13,>F0
1 SEC LOADED IN SZ DURATION
2 64 E
2650
0 OFO
A34 i
4
4
4
AGAIN
FUNCTIONAL LOOP
A 1.13
ADD NEW PERIOD TO SZ DURAT
2652
0 4C1
CLR
1
CLEAR R. RATE COUNTER
2654
C4E0
CLR
SDELAY
CLEAR SPIKE LOCATION
2656
2653
FC 00
06 AO
3L
SPEAK
GO TO PEAK
265 A
265C
23A0
0281
Cl
1 ,HRATE
DESYNCHRONIZATION7
2 65E
2 66 C
2662
2664
2666
2668
0080
l 503
0281
0034
1 1 05
C3G1
JGT
Cl
JLT
MOV
MISS
1 ,LRATE
MI SS
1 .SViSTA 1
PASS R. RATE TO STATIS
2 66 A
266C
FO AO
C420
3LWP
SSTAT1
266E
2670
2672
FCOE
1 OEF
0281
MI SS
JMP
Cl
AGAIN
I .LONG
1 SEC WITHOUT S.W.?
2674
2676
2678
0 120
1500
4541
JGT
A
ZOUT
1,13
NO,UPDATE DURATION
267A
0 4Cl
CLR
1
CLEAR R. RATE COUNTER
2 67C
267E
2630
04E0
F COO
06 AO
CLR
BL
SDELAY
SPEAK
NEXT SW. WITHIN LIMITS?
2682
2684
2686
2688
2.3 A 0
0231
0 060
1 504
Cl
JGT
1 ,HRATE
ZOUT
NO,END SZ
268 A
268C
268E
0281
0034
1101
Cl
JLT
1 LRATE
ZOUT
2690
1 OOF
JMP
AGAIN
YES,RESTART CLEAN
2692
CF8D
ZOUT
MOV
13,414+
STORE SZ DURATION


Fig. 5b. 4th Order Filter. Canonic Implementation.


306
2324
0202
LI
2 *>2C
MIDDLE PERIOD I
2226
002C
2328
0 4C5
CLR
6
2 22 A
C 0 02
MOV
2.3PEP. 10
222C
FCOA
2 32E
0204
L I
4, >F0
2330
OOF 0
2332
0 2 EO
LWPI
MAIN
2334
FDSO
2236
0 4C6
CLR
6
2333
0 4C5
AGAI N
CLR
e
233A
04C1
AG AI N1
CLP
1
233 C
CS06
MOV
6 3DETEC
NO DETEC FLAG
2 33 E
FC03
234 C
C30A
MOV
10.3PWAVE
OLD PERIOD IN P'
2 34 2
FCOC
2344
C l 85
MOV
5 6
UPDATE DETEC FLA
2 34 6
C2S9
MOV
5.10
UPDATE PERIOD
2348
06 AO
BL
SPEAK
GET NEXT PERIOD
224A
23E0
234C
0281
CT
1 .HRATE
WITHIN LIMITS?
234 E
00 15
2 3 50
1 5F3
JGT
AGAIN
2352
0281
Cl
1 >LRATE
2354
0 0 OF
2356
1 IF 0
JLT
AGAIN
2353
0205
LI
5, l
DETEC FLAG
235 A
0001
235C
C 2 4 1
MOV
I .9
UPDATE PERIOD
2 35 E
10 ED
JMP
AGAIN1
END
NC.CF ERRORS IN THIS ASSEM3LY= 0000
RELOCATABLE LOCATIONS USED = 0000


61
|C|+|D|<1 (23)
which is shown in Fig. 3b as the square hatched. This con
dition is very restrictive for most applications; therefore,
most of the practical designs will display the undesirable
effect of overflow propagation.
Since the overflow is a nonlinearity in the system, it
can be expected that various implementations (different
ways of calculating the recursion relation) will display
different overflow properties. The parameters one can
choose to control the overflow are special type of adders,
scaling, and exploring topologic differences in the struc
tures .
When the result of an addition is bigger than the
register length in two's complement representation, there
is an abrupt change in sign. It has been shown (Fettweis &
Meerkitter, 1972) that at least for the class of wave
digital filters, saturation arithmetic allows for the
absence of parasitic oscillations. Here saturation arith
metic means the type that holds the signal at maximum level
when an overflow occurs. This implies that overflow must
be monitored. The relations between the type of saturation
arithmetic, distortions at the output and stability are a
present area of research (Claasen et al., 1976). No general
results are available.
Scaling the signal level is the most general way to
handle overflow. To prevent adder overflow the input, xn,


316
TITL 'ST ATIS
****$#£ **#:*:**:$**:**** ********* ***
* STATI51
**** $3¡c* *** ¡fe*#*******#*:** *:£ *****
* THIS PROGRAM IS TO BO USED IN
* CONJUNCTION WITH TOTALS
* IT CALCULATES THE MEAN AND VARIANCE
* OF A PARAMETER ASSUMED IN RO
*
2530
FC22
FLAG
AORG
EQU >F
>2580
C2 2
2530
C 320
MOV
~*"2FLAG. OF'LA
2582
2534-
2 53 6
FC22
FC22
1608'
JNE
FINI
2538
A 030
A
0,2
253 A
1T 0 l
JNC
S MAL 1
2 53C
0531
I NC
1
253 E
0583
SMAL 1
INC
3
2590
Cl 80
MOV
0,6
2 59 2
3930
MPY
C
2594
A1 06
A
6,4
2 59 6
A 147
A
7 ,5
255 3
1701
JNC
SV.AL2
259 A
0534
INC
4
2 SSC
0380
5MAL2
RTWP
259 E
3C43
FIN I
D I V
3, 1
25AC
3D03
DIV
3,4
22A 2
19 OF
JNO
SMALL
2 5A4
0 A43
SLA
3,4
2SA6
3D 03
DIV
3 ,4
25A 3
C 131
MOV
1 ,6
25 AA
C081
MOV
1,2
25AC
3831
MPY
1 ,2
2 5 A E
0AC2
SLA
2, 12
2 53 0
0943
SRL
3 ,4
2 53 2
E0C2
SOC
2,3
2534
6103
5
3,4
2SS6
C 046
MOV
6,1
2508
0200
t. I
0 ,>C
.2 53 A
2 SBC
OOOC
CACO
SLA
0 ,>c
25BE
EO 40
SOC
0, 1
2 5C0
25C2
0330
C 08 1
SMALL
RTV/F
MOV
1 ,2
25C4
3881
MPY
1,2
2 5C6
61 03
S
3 ,4
25C3
0330
RTWP
END
#


Abstract of Dissertation Presented to the
Graduate Council of the University of Florida
in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy
AUTOMATED DETECTION AND QUANTIFICATION
OF PETIT MAL SEIZURES IN THE ELECTROENCEPHALOGRAM
By
Jose Carlos Santos Carvalho Principe
August 1979
Chairman: Jack R. Smith
Major Department: Electrical Engineering
This dissertation deals with the automated analysis,
and quantification of Petit Mai (PM) paroxysms in the human
electroencephalogram (EEG). A petit-mal detector was built
to help neurologists evaluate drug effectiveness in the
treatment of PM epilepsy. The decision of basing the
detection scheme in a microcomputer provided completely new
directions for the design process because of the versatil
ity and great computational capabilities of the machine.
The problem of nonrepeatability of characteristics in
the analog filters was avoided by replacing them by digital
filters. A microcomputer based digital filter design pro
cedure was developed, taking into consideration the compu
tation speed, the filter internal gain and the noise
characteristics of different topologic structures. To
yield sufficient output signal to noise ratio a 16 bit
vi


CHAPTER I
LITERATURE SURVEY
Two research methods have been applied to automated
electroencephalogram (EEG) studies: spectral analysis and
time domain analysis. It is the purpose of this chapter to
survey the basic different techniques and assumptions
involved and to present a better picture of the advantages
and limitations of each method. Our attention will be
mainly focused on techniques used or related to detection
of pathological paroxysmal events in the EEG, and the
literature referenced herein denotes this emphasis.
Spectral Analysis
Before addressing this subject, let us first summarize
the general assumptions made about the EEG that validate
the application of the technique. The theory behind the
frequency domain approach using a nonparametric model, as
in conventional power spectral analysis, handles the EEG
signal as a stochastic process. The statistical properties
of the process essentially influence the analytical
results. One major difficulty is exactly the different
opinions about the stationarity and Gaussian behavior of
the EEG process which are prerequisites to carry out spec
tral analysis and to use the power spectrum as a sufficient
1


159
Procedure:
1 Tape Recorder to Play Mode (in
Leader)
2 Press Return in Terminal
3 Extension Port Switch to Reverse
4 When Finished Switch to Neutral
Fig. 29.
Load from Tape Recorder to Microcomputer


244
If the attenuation
log (w+Zw^-l)
is given in dB/octave, at w=2
= log (2+/3)
and
i 22
1+e T
n
w=2
attenuation =
10
A
10
where A is in dB. Therefore,
T.
n
e
and (11) becomes
n
log
/ A/10
2 10
£
log (2+/3)
(1-12)
The procedure to determine the Chebyshev lowpass goes as
follows:
1) From a given ripple factor (e) in the passband,
can be obtained from (9) and sin hcf> and cos h
M fa
from (10).
2) The polynomial order is obtained from the attenua
tion in dB/octave using (12).
Filter Design Program
The Fortran IV program, which calculates the Z plane
bandpass filter poles quadratic factors and number of zeros


125
(10 volts full scale). Being aware of the fact that these
filters will not be input response stable (due to the pole
locations), the input signal level was selected such that
tape recorder saturation level will correspond to A/D full
scale. Fig. 16 shows the performance of both filters in a
typical PM epoch.
Selection of the Slow Wave Period
According to the EEG literature, the slow wave, if
modelled as half a sine wave, can be expected to have a
period of 0.1 to 0.25 sec (corresponding to frequencies of
2-5 Hz). These were the first set of parameters imple
mented. Two methods were used to measure the period of the
waves. One used standard zero crossing (Fig. 17) by count
ing the number of samples between points B and D, and the
other measured peak-to-valley times, i.e., number of
samples between points A and C. After comparing both
methods on a set of seizures from four patients, it was
concluded that the peak to valley measure was more reliable
in the sense that the period window was smaller to accommo
date all the patterns (the larger window detected alpha
waves as in-band signals). There is a morphologic expla
nation for thisthe slow waves are not sinusoidal, and the
positive going edge of the dome is a function of the repe
tition rate and of the appearance of the first spike.
There is also a signal processing reason: As in the PM
paroxysms there are high frequency components of large


118
characteristics of both designs are also shown in Table II.
As expected, the wide-band displays smaller magnification,
keeping the ripple and 3 dB points almost unchanged. How
ever, the roll-off is slower. The comparison of the per
formance of both slow wave filter designs is shown in
Fig. 14a. It can be said that the narrow-band design works
better since the filtered output resembles more a periodic
waveform; i.e., the "blimp" produced by the spike component
is smaller. The spike narrow- and wide-band were also
compared with respect to ringing (a square was utilized).
The steady state characteristics are similar. However, the
wide-band tends to have a longer decay in the impulse
response (Fig. 14b). A scaling of 3 bits is necessary to
accommodate the narrow-band realization with the hardware
available (i.e., 12 bit A/D and 16 bit microcomputer). If
the scaling is done at the input (input wordlength 9 bits),
the simulation shows that the output S/N ratio will be
comparable (K>1), i.e., 48 dB. However, the scaling of
three bits was performed within the resonators, improving
considerably this figure.
Besides the general tests of frequency and impulse
response of the filters shown in Fig. 15, the limit cycle
behavior was also analyzed. With the A/D inputs short-
circuited, the filter output was periodic with a period
roughly twice and three times the center frequency (limit
cycle of second and third order) for the spike and slow
wave respectively. The amplitudes were of 10 and 5 mV


163
TABLE III
SYSTEM REPEATABILITY
SEIZURE I (PATIENT #7)
Repetition Slow Wave Spike
Duration Period 1/2 Period Delay Amp Amp
x a2
x O'2
x cr2
xi
Q
to
x a2
EC1
4 A
101
18
36
1C
BA
9E
4D5
EA
EFl
F21
49
FD
18
35
1C
D3
9E
4CF
E9
FAO
EBB
4A
EC
18
IF
1C
c8
9F
1RO
E5
94C
SEIZURE II (PATIENT #12)
1D04
5E
151
26
11B
31
4DF
75
522
5B
2A3
1D07
5E
116
26
121
2F
53F
75
4C3
57
250
SEIZURE III (PATIENT #7)
123F
47
F3
18
79
1A
3C
99
C70
F7
760
1245
49
B7
19
2B
1A
2B
9C
6F0
F9
AF3
1245
4B
F7
19
2C
1A
3D
AO
5C6
FB
977
UNITS: Number of points (hex), 1 sec = FO, except for
amplitude (filter output in hex).


343
Serafina. f M. "A Pattern Recognition Method Applied to EEG
Analysis. Computers and Biomedical Research, 6:187-
195, 1973.
Shepard, R. N., and J. D. Carroll. "Parametric Representa
tions of Nonlinear Data Structures." In Proc. Int.
Symp. Multivariate Analysis. Academic Press, New
York, 1966.
Smith, J. R. "Automatic Analysis and Detection of EEG
Spikes." IEEE Trans. Biomed. Engng., BME-21:l-7,
1974.
Smith, J. R. "Computers in Sleep Research." Critical
Reviews in Bio-Engineering. CRC Press, December 1978.
Smith, J. R. "Digital Filtering Techniques for EEG Proces
sing." Internal Report, Clinique Bell Air, University
of Geneva, Switzerland, 1979.
Smith, J. R., Negin, M., and A. H. Nevis. "Automatic Anal
ysis of Sleep EEG by Hybrid Computation." IEEE Trans.
Systems Science Cybernetics, SSC-5:278-284, 1969.
Smith, J. R., Funke, W. F., Yeo, W. C., and R. A. Ambuehl.
"Detection of Human Sleep Waveforms." Electroenceph.
Clin. Neurophysiol., 38:435-437, 1975.
Smylie, D. E., Clarke, G. K. C., and T. J. Ulrych. "Analy
sis of Irregularities in the Earth's Rotation."
Methods of Computation Physics, 13:391-394, Academic
Press, 1973.
Stevens, J. R., Kodama, H., Lonsbury, B., and L. Mills.
"Ultradian Characteristics of Spontaneous Seizure Dis
charges Recorded by Radio Telemetry in Man." Electro
enceph. Clin. Neurophysiol., 31:313-325, 1971.
Szczupack, J., and S. Mitra. "Recursive Digital Filters
with Low Roundoff Noise." Circuit Theory and Applica
tions 5:275-286, 1978.
Szczupack, J., and S. Mitra. "Digital Filter Realization
Using Successive Multiplier Extraction Approach."
Trans. Acoust. Speech, and Signal Proces., ASSP-23:235-
239, 1975.
Tausworthe, R. Standardized Development of Computer Soft
ware. Prentice Hall, New Jersey, 1977.
Temes, G. C., Barcilon, V., and F. C. Marshall. "Optimiza
tion of Bandlimited Systems." IEEE Proceedings,
61:196-234, 1973.




42
(Blinchikoff, 1976). In the narrow-band, the lowpass
filter poles are transformed by the relation
(4)
where w,, w, are the upper and lower cut-off frequencies
and Wg the center frequency.
pairs are
given by
a>0
Pair 1
w0 t-Ja+bj(j6-a)]
Pair 2
wQ [-^a-bj(X6+a)]
where
. y2 2 2.
Y 2 2
A = l-Va -B )
4
For the wide-band the poles
a<0
w0[-^a+bj(J$+a)]
wQ[-Ja-bj(jB-a)]
aBY2
2
a
r2 2
/a +B
2
+A
b
U2
A +B
-A
and the lowpass poles are -aj3. Here the transformation
of the poles is stressed since it will avoid polynomial
factorization to obtain the bandpass digital filter in a
cascade form.
The two transformations possess quite different prop
erties, the most important for this application being the
different Q of the poles. Looking closely at (4) it can be
seen that the bandpass poles lay on a parallel to the jw


11
very sensitive to rounding (Box & Jenkins, 1970) mainly for
random processes that display peaking power spectrum, which
means that the resolution obtained is not always enough.
This is to be expected since the YW technique effectively
windows the data. The Burg technique does not display this
shortcoming of lack of resolution. It has been shown
(Pusey, 1975) that it can resolve two tones arbitrarily
close if the S/N ratio is high enough. However, the var
iance of the estimator is larger than for the YW and does
not decrease to zero monotonically.
The correct identification of the order of the AR
model that approximates the data is vital in the computa
tion of the power spectrum (Ulrich & Bishop, 1975). The
criterion generally used is Akaike's Final Prediction error
(FPE) that is defined as the mean square prediction error
(Akaike, 1969, 1970). The YW estimate of the order of the
process using this criterion tends to be conservative but
with a small variance. The Burg estimate of the order dis
plays a large variance, so generally some upper bound must
be imposed in the search. Another approach is to use the
first minimum in the estimated error (Ulrich & Bishop,
1975).
While the AR model is an all-pole approximation to the
random process, the ARMA model is a pole-zero approxima
tion. Computationally it is the more expensive (in time
and memory dimensions) and more difficult to implement, but
the two techniques for AR computations could be modified


338
Gotman, J., and P. Gloor. "Automatic Recognition and
Quantification of Interictal Epileptic Activity."
Electroenceph. Clin. Neurophysiol., 41:513-529, 1976.
Grass, A. M., and F. A. Gibbs. "Fourier Transform of EEG."
J. Neurophysiology, 1:521-526, 1938.
Hagne, I., Persson, J., Magnusson, R., and I. Petersen.
"Spectral Analysis via FFT of Waking EEG in Normal
Infants." In Automation in Clinical Electroenceph.
Raven Press, New York, pp. 103-143, 1973.
Harner, R. N. "Sequential Analysis and Quantification of
the EEG." Electroenceph. Clin. Neurophysiol., 34:791,
1973.
Harner, R. N., and K. A. Ostergren. "Sequential Analysis
of Quasistable and Paroxysmal EEG." In Quantitative
Studies in Epilepsy. Raven Press, New York, pp. 343-
354, 1976.
Helstrom, C. W. Statistical Theory of Signal Detection.
Pergamon Press, New York, 1968.
Herolf, M. "Detection of Pulsed Shaped Signals in EEG."
Technical Report No. 41, Telecommunication Theory
Royal Inst, of Technology, Stockholm, 1973.
Hwang, S. Y. "Roundoff Noise in State Space Digital Fil
ters: A General Analysis." IEEE Trans. Acoust.
Speech, Signal Proces., ASSP-24:256-267, 1976.
Isaksson, A. "Visual Evaluation and Computer Analysis of
the EEGA Comparison." Electroenceph. Clin. Neuro
physiol. 38:79-86, 1975.
Isaksson, A., and A. Wennberg. "Spectral Properties of
Nonstationary EEG Signal by Means- of Kalman Filter
ing. In Quantitative Analytic Studies in Epilepsy.
Raven Press, New York, pp. 389-402, 1976.
Jackson, L. B. "Roundoff Noise Analysis for Fixed-Point
Digital Filters Realized in Cascade or Parallel Form."
IEEE Transactions on Audio and Electroacoustics,
AU-18:107-122, 1970.
Jenkins, G. M., and D. G. Watts. Spectral Analysis and Its
Application. Holden-Day, San Francisco, 1969.
Jestico, J., Fitch, P., Gilliatt, R. W. G., and R. G.
Willison. "Automatic and Rapid Visual Analysis of
Sleep Stages and Epileptic Activity." Electroenceph.
Clin. Neurophysiol., 43:438-441, 1976.


APPENDIX III
FLOW CHARTS AND PROGRAM LISTINGS



Q)
U>
Fig. 40b.
r-
KO
o
O
R. Period Versus Duration (#5-2)
210


79
in parallel with the corresponding filter (Rabiner & Gold,
*
1975). The second approach is to study each individual
filter separately and optimize the pole locations by com
paring the transfer functions of the filter realized with
high coefficient precision and the one obtained with the
actual values. Rabiner and Gold present experimental
results for the error as a function of the wordlength.
The table for cascade realization is shown in Fig. 8. For
filters realized as a cascade of second order structures,
2
the normalized error variance is below 10 for wordlengths
of 16 bits. This is considered a very good practical
agreement. The degradation is very steep towards shorter
wordlengths, the variance being 8 to 10 bit coefficients.
Therefore, 16 bit coefficients are thought necessary for
practical designs.. The extrapolation of their results for
any filter realized as a cascade of second order sections
is not adequate, since the grid of possible pole locations
inside the unit circle is not constant. The grid is
defined by the intersections of concentric circles corre-
2
spondmg to the quantization of r and straight lines cor
responding to quantization of r cos 0 (standard complex
notation is used). The density of pole locations is less
in regions close to the real Z axis as can be shown in the
following way. Consider a filter with pole pair (L,K)
where


251
written in any other 16 bit microprocessor for comparison,
the execution time is considered fast. The main reason is
the frequent change of workspaces and the relatively small
dimension of the program loop, as is going to be shown
next. For each second order filter structure, the filter
coefficients (2) and three (3) previous values (2 for the
past value of the output and one for the previous value of
the input) for a total of 5 quantities need to be carried
from the previous iteration. With the modularity of the
workspaces, each time the computation of one resonator is
needed, the corresponding workspace address is loaded in
the WSPan instruction that takes 4 ys. The program pur
sues without the need to save the previous state of the
machine or bringing in the 5 values from the previous iter
ation. As the program for each resonator is only 14
instructions long, this represents a considerable savings.
In Fig. II-l the basic microcomputer configuration to
perform the real time filtering function is displayed. A
12 bit I/O board (Analog Devices RTI 1240) was used in a
memory mapped I/O configuration. It plugs directly in the
TI bus and can be configured by software. The main options
are the amplifier gain (set at 1:1) and the auto indexing
channel feature (not used). The utilization consists of
initializing a conversion (write to base addr + Ajj) check
ing the end of conversion flag (bit 0 of base addr + C^)
and transferring the converted data, which appear in base


187
Table VI shows that the detector was able to give
similar clinical information for every patient analyzed.
The major difference is displayed in #5, and it is due to
false detections in the first two sessions.
Statistics of Seizure Data
One of the great advantages of automated detection in
EEG studies is the system's ability to detect waves that
will meet standard definitions which are not allowed to
vary subject to the context or learning experience. The
computer inherently includes a quantitative description of
what is detected. Hence, it can be used to analyze objec
tively the data. Up to the present most of the real time
detection schemes for EEG analyses have an on-off type of
output; i.e., they just convey the information about pres
ence or absence of the type of waves they are programmed to
detect.
The advent of microcomputers can radically change this
picture, because they allow the implementation, at low
cost, of powerful signal processing algorithms that run
real time. In a digital algorithm such as the one utilized
for the PM detector, every sample of the input is analyzed
and its information is condensed in higher value structures
like waves and patterns. Subsequently, when a wave is
detected, there is available, in the microcomputer memory,
the information regarding the parameters used to recognize
it. For instance, for the detection of a slow wave, where


85
can be defined and enables direct comparisons between
structures and designs, since it is independent of the in
put noise variance. The value K<1 sets the boundary for
the case where the noise created by the digitalization and
the calculations will degrade, in a r.m.s. sense, the in
put (analog) signal to noise ratio. The output signal to
noise ratio (peak signal power to r.m.s. noise) can be
obtained from (47) through a multiplication by A /at where
A is the input signal amplitude. This definition of S/N
ratio seems appropriate for EEG signal processing since the
various signals of interest are narrow-band and fall in the
filter passband.
The filters being of order four, an exhaustive search
to find the best cascading of sections and best pole zero
pairing was possible. The Dinap program (Bass et al.,
1978) was extensively applied to access the noise (and mag
nification) properties of different structures. Fig. 9
shows a typical output. In (Balakrishnan, 1979) a detailed
explanation of the program and its use is presented.
Practical Considerations
Processing Speed
In the internal magnification section it was said that
the filters were going to be implemented with a computation
wordlength bigger than the input number of bits. This is
not the general way of filter implementation, which scales


47
implementation with simple adders (or subtractors) which
are fast and do not contribute any roundoff errors.
It may be expected that the Z domain filter character
istics will not display constant gain across the passband,
since a linear relation was used to map the poles and now a
zero is being placed at w=wg/2. To compensate for this
fact, one technique places a different number of zeros at
z=l, according to the relation (Childers & Durling, 1975)
1+cos W-.T
k = £_ (9)
1-cos wcT
where wc is filter center frequency.
Bearing in mind the discussion of the lowpass to band
pass transformations, it can be expected that the narrow-
band will compensate in part the asymmetry since the high
frequency pole has already a higher Q than the low fre
quency one. It turns out that the narrowband transforma
tion used with the direct substitution requires one zero at
each of the locations. The number of zeros required for
the other combinations (i.e., direct substitution with
wideband transformation and bilinear) is shown in Table I
for second order filters. From the results obtained with
the EEG filters (Principe et al., 1979) it can also be con
cluded that the sensitivity of the passband gain to differ
ent location of the filter center frequency is much lower
than (9) predicts.


9
The eigenvalues extracted from the parametric time series
model of the EEG are the characteristic frequencies and
their associated damping factors. The damping reflects the
extent to which the EEG will exhibit an oscillatory or ran
dom appearance. Unlike nonparametrie (conventional) spectra
analysis, the relative dominance of the frequencies in the
EEG can be associated with the ordering of the magnitudes
of the eigenvalues.
In the AR model, the linear system transfer function
is approximated by an all-pole function. The two problems
are the determination of the filter poles location and the
order of the approximation polynomial. There are three
main minimization procedures to fit the AR model to the
data: one evaluates the filter coefficients as the maximum
likelihood estimate when the input to the linear system is
white Gaussian noise and the output is the data sequence
available (maximum likelihood method). Another evaluates
the filter coefficients in such a way that the mean square
error between the next sample and the predicted one, given
the data sequence, is minimized (linear prediction). Fi
nally, the other calculates the filter poles in such a man
ner that the estimated values of the sequence maximize the
entropy of the autocorrelation function (maximum entropy).
The three methods have been developed under different con
straints, but recently van den Bos (1971) and Smylie et
al. (1973) proved their equivalence. It is also inter
esting to note that all the methods arrive at the same


Input 0.1 volts (10 V P.P.)
Fs=240 Hz. Linear scales.
Fig. 15c. Spike Bandpass Filter Frequency Response
123


114
be taken to select the bandwidth since high Q filters ring.
The annoying effect of ringing can be understood if the
output is viewed as the convolution of the input with the
impulse response of the system. Any sharp transient at the
input which will resemble a delta function will produce an
output equal to the impulse response. As the impulse
response of any bandpass filter is a damped sinusoid (or a
combination thereof), the zero crossing information of the
response to a delta function may be recognized as an in-
band signal. An amplitude criterion in conjunction with
the zero crossing information may be successfully used in
differentiating between in-band rhythmic activity and out-
of-band fast activity provided the impulse response is of
low amplitude and with damped frequency distinct from the
natural frequency of the system. Impulse response of high
Q filters possess neither of these characteristics.
Another way of saying the same thing is the following:
For high Q filters the steady state attenuation character
istics may be very good, but the response of the system to
high frequency transients mimics a considerable number of
cycles of in-band sinusoidal activity, so further processing
of the filtered data through zero crossing is useless. In
EEG processing this is a very important point since muscle
activity is faster than the EEG activity and can be of much
higher energy. Low Q filters followed by zero crossing
detection have been found much more reliable. The steady
state attenuation is inferior when compared to high Q


89
the signals within the filter structure. It has been shown
(Jackson, 1970) that scaling uses more efficiently the com
putation wordlength. The values for the scaling factors
Gl' G2' an(^ G3 are ^>ta^ne<^ from the internal magnification
analysis. In the scaling design the zeros can no longer be
realized as simple adders (subtracters). To use the full
dynamic range of the processor the zeros shall be realized
as multipliers, increasing the required number from 4
(Fig. 5c) to 9 (Fig. 5d). In a microcomputer implementa
tion this increase slows down drastically the computation,
because the multiplication is by far the most time consuming
operation. To save computation time, the multiplications
can be approximated by shift operations (Oppenheim &
Shafer, 1975), but it defeats the purpose of the design
procedure. Even in this case, the network complexity in
creases appreciably (5 more operations per cycle). It can
be concluded that scaling better uses the dynamic range at
expenses of longer computation times. In (Principe et al.,
1979) the results were presented for the class of EEG fil
ters which show that with the nonscaling design only one
extra bit is needed to obtain the same output signal to
noise ratio. Therefore, for the microcomputer implementa
tion the increase in computation time was thought more
demanding than the nonoptimum use of dynamic range.
The nonscaling design coupled with a careful filter
design enables the implementation of the class of EEG


148
three slow waves with the prescribed repetition rate, it
checks if a spike has also been detected (is DELAY greater
than 0.6 sec?). If not, the program restarts the search.
If all conditions are met, a positive pulse is outputted to
D/A I, and control is passed to SZURE. At the end of
SZURE, a negative pulse is outputted to D/A I, and MAIN is
restarted.
PEAK. This program uses the same workspace as MAIN.
It is linked through a BL instruction. As the program is
in continuous operation, overflows of the repetition rate
counter and of the spike recognition location can occur.
This is monitored in the beginning of PEAK. After passing
control to the FILTER program,- valid data appear in R2 and
are outputted to D/A I. Control is then passed to SPIKE
program (BLWP). When it returns to PEAK, the algorithm to
detect the peak begins. When a (+,-) transition is
detected, the program initiates a search. Control is in
the first loop of the program when the filtered data are
decreasing. When a negative peak is reached, two counters
are initiated. R4 counts the valley-to-peak time and R9
the zero crossings period. Control is then in the second
loop that recognizes the increasing slope of the wave. The
zero crossing is detected along with the peak. This loop
is the most involved since from the valley (-) to the peak
(+) the waveform is not monotonic (see Fig. 14). Irregu
larities (e.g., change in slope) in the negative portion of
the wave are allowed but not in the positive. When the


292
TITL 'SZURE
** *::# *'(* ****:** £*****
* SZURE
**:*- *.**.*£.* **
* CONTROL IS PASSED
* RECC0NIZE5
* ALLOWS FOR
* STATISTICS
* PARAMETERS
* CONTROL IS
* AND
REGISTERS





ST ATIS
USED
R1 R. RATE COUNTER
R13 SZ DURATION
R14 MEMORY POINTER
PI5 AMPLITUDE THRES
FROM MAIN.
END OF SZ AND
DESYNCHRCNIZATIONS
OF DETECTION
ARE GENERATED.
PASSED TO PEAK (8L)
(3LWP)
FC24
SZT I M
EQU
>FC24
2324
SZOUT
ECU
>2324
FC04
THRES
EQU
>FC04
23 AO
PEAK
EQU
>23 AO
FD 80
MA I N
EQU
>FD80
0080
HR AT E
EQU
>80
0034
LR ATE
EQU
>34
0 120
LONG
EQU
>120
FCOO
ELAY
EQU
>FCOO
FD AO
V*STA 1
EQU
>FD A 0
FCOE
ST AT 1
EQU
>FCOE
FC12
ST AT 2
EQU
> FC1 2
FC16
STAT3
EQU
>FC 1 6
FC 1A
STAT 4
EQU
>FC.l A
FC1E
STATS
E QU
>FC1 E
FC 22
FLAG
EQU
>FC22
FF9C
TIME
EQU
>FF9C
FC2A
ARTI F
EQU
>F C2 A
0 2 DO
SZMIN
EQU
>2D 0
0 03C
TPLUS
EQU
>3 C
00 14
TMt MU
EQU
>14
0960
TEN
EQU
>960
FC2A
LESS 3
EQU
>FC2 A
FC2C
LES 1 0
EQU
>FC2C
FC2E
GRT1 0
EQU
>FC2.S
2620
C2E0
LWPI MAIN
2622
FD80
2624
02 0E
LI
14 >FDAO
2626
F DAO
2628
02 OD
LI
13 >A0
262A
OOAO
262 C
04 FE
LOOP
CLR
14+
CLEAR ST ATIS WSP


321
2064
C182
SACK
MOV
2, 6
2 06 6
8042
C
2.1
REACH END?
2068
l 3 2A
JEQ
OUT
2 06 A
0226
AI
6,4
2 C6C
0004
2 06E
8006
C
*6,3
SMALL SZ?
2070
1614
JNE
BIG
2072
COOO
MOV
0,0
INTERESTED IN SMALL SZ?
2074
160F
JNE
CONT
2076
Cl 82
MOV
2,6
R6 IS MEM POINTER
2078
A IA0
A
BAODX.
207 A
FCOO
207C
C316
MOV
*6,12
R 12 GETS OAT A
207E
A 1 AO
A
8AOO Y, 6
208 0
FC02
2082
C 396
MOV
*6,14
R14 GETS YDATA
2084
C208
MOV
8, 3
FINAL PASS?
2086
1302
JEQ
CONTI
2038
0409
BL WP
9
PLOT IT
203 A
1004
JMP
CONT
2G3C
06AO
CONTI
BL
a MAXX
208E
2002
2090
OoAO
BL
3MAXT
FIND MAXY
2092
2 ODA
2 094
0222
CONT
A I
2, 6
UPDATE MEM POINTER
2 096
0006
2CS3
1 0E5
JMP
BACK
2 09 A
Cl 82
8IG
MOV
2,6
209C
A1 AO
A
BADOX,6
209E
FCOO
20 AO
C316
MOV
*6, 12
20A 2
A 1 AO
A
3ADDY,6
20 A 4
FC02
20A6
C396
MOV
*6,14
2 OA 8
C208
MOV
8 ,S
20 A A
1302
JEQ
CONT 3
2 0AC
0409
3LWP
9
2 OAE
1004
JMP
CONT 2
2030
06 AO
CONT 3
3L
IM AXX
2 OB 2
2002
2034
C6A0
BL
2MAXY
20B6
2 ODA
2C8 8
0222
CONT 2
AI
2 > 1 A
208 A
00 1A
2 OB C
1 003
JMP
BACK
2 08 E
C208
CUT
MOV
3,3
20C0
1606
JNE
FINI
2CC2
02 08
LI
8,1
2 0C4
0001
20C6
0409
3LWP
9
DRAW THE AXIS
2 0C8
02 OA
LI
10 ,>222A
SKIP AXIS NEXT TIME
20CA
222A
20CC
1 0C9
JMP
BEGIN
20CE
0460
FINI
3
3MCNIT
2000
0080
*
*
MAXX
2 002
834C
$
MAXX
c
12,13
2004
1101
JLT
C0NT5
2006
C34C
MOV
12, 13
Rl3 GETS MAXX
2 0D8
045B
C0NT5
*
B
*1 1
*
*
MAXY
2 00 A
83 CE
Â¥
MAXY
C
14, 15
2 OOC
1101
JLT
C 0 NT 6
200E
C3CE
MOV
14,15
R15 GETS MAXY
2 OE 0
0450
CO NT 6
g
END
*1 1


344
Tharp, B. R. "Autoregressive Spectral AnalysisA Unique
Technique for the Study of Human Seizure Activity."
Computers in Biomedicine, 5:26-29, 1972.
Tharp, B. R., and W. Gersch. "Spectral Analysis of Seizure
in Humans." Computers in Biomedical Research, 8:503-
521, 1975.
Thomas, J. B. Statistical Communication Theory. Wiley,
New York, 1969.
TMS 9900 Microprocessor Data Manual, Texas Instruments,
Inc., 1976.
Treitel, S., Gutowsky, P. R., and E. A. Robinson. "Empiri
cal Spectral Analysis Revisited." Topics in Numerical
Analysis, vol. 3, Academic Press, 1977.
Ulrich, T. J., and T. N. Bishop. "Maximum Entrophy Spec
tral Analysis and Autoregressive Decomposition."
Reviews of Geophysics, 13:183-200, 1975.
Van den bos, A. "Alternate Interpretation of Maximum
Entrophy Spectral Analysis." IEEE Trans. Info.
Theory, IP-17:493-494, 1971.
Vera, R. S., and W. T. Blume. "A Clinical Effective Spike
Recognition Program." Electroenceph. Clin. Neurophy-
siol., 45:545-548, 1978.
Viglioni, S. S. "A Methodology for Detecting Ongoing
Changes in the EEG Prior to Clinical Seizures."
McDonnel Douglas Astronautics Company, paper APA 74,
133, 1974.
Walter, D. 0. "Spectral Analysis of EEG: Mathematical
Determination of Neurophysiological Relationships from
Records of Finite Duration." Experimental Neurology,
8:155-181, 1963.
Walter, D. 0., Rhodes, J. M., Brown, B. S., and W. R. Adey.
"Comprehensive Spectral Analysis of Human EEG Genera
tors." Electroenceph. Clin. Neuroohysiol., 20:224-
237, 1966.
Walter, D. 0., Rhodes, J. M., and W. R. Adey. "Discrimi
nating among States of Consciousness by EEG Measure
ments: A Study of 4 Subjects." Electroenceph. Clin.
Neurophysiol., 22:22-29, 1967.


Fig. 47. Amplitude Spike Versus Amplitude Slow Wave (#7-1)
223


Fig. lib. PM
Variant (Patient #4)
104


278
(SPIKE^
V Start J
R6 pointer to
Main WSP
'if
Save sign of
input (R4).
Get sign of
new point.
V
Load PC for
next jump.
(
*
Return
)


xml record header identifier oai:www.uflib.ufl.edu.ufdc:UF0008246100001datestamp 2009-02-24setSpec [UFDC_OAI_SET]metadata oai_dc:dc xmlns:oai_dc http:www.openarchives.orgOAI2.0oai_dc xmlns:dc http:purl.orgdcelements1.1 xmlns:xsi http:www.w3.org2001XMLSchema-instance xsi:schemaLocation http:www.openarchives.orgOAI2.0oai_dc.xsd dc:title Automated detection and quantification of petit mal seizures in the electroencephalogramdc:creator Principe, Jose Carlos Santos Carvalhodc:publisher Jose Carlos Santos Carvalho Principedc:date 1979dc:type Bookdc:identifier http://www.uflib.ufl.edu/ufdc/?b=UF00082461&v=0000106808347 (oclc)000098613 (alephbibnum)dc:source University of Floridadc:language English


153
fs=240 Hz is obtained by loading 187.. in CRU bits 1-12. To
II
leave the wait loop in FILTER, PC is incremented before
returning. Workspace of interrupt III (FF8A ) is used. R9
H
is the seconds counter.
CALIB. This program is identical to the first loops
of PEAK to determine the amplitude of the peak of the wave.
It is recursive 64 times to give stable readings. The
values of the peaks are multiplied by the filter gains and
normalized such that the thresholds are set at 75 uV.
These numbers are then stored in THRES and SPTHR.
System Output
For testing purposes, the output of the slow wave fil
ter was chosen as one of the outputs of the system (D/A I).
The other D/A was used to output the detection flags, nega
tive pulses (upward) for slow wave detection, positive
(downward) pulses for spike detection. Another critical
parameter is the beginning and end of seizure flags. Since
there were only two D/A available, it was decided to use
also D/A I to output a fast positive pulse in the beginning
of seizure and a negative pulse when the seizure ends.
Although two informations are multiplexed in D/A I, they
are easily identified as the output of the slow wave is
not "spiky." Fig. 27 shows a typical output. For the
detector (statistics) the seizure duration is considered
1 sec before the place where the negative going pulse in
Channel II appears (three slow waves with a 3 Hz repetition


3
the segments are highly non-Gaussian, higher order statis
tics as bispectra (Dumermuth et al., 1970) could be needed.
Undoubtedly, the early work on EEG quantification of
Grass and Gibbs (1938), Walter and coworkers (1963, 1966,
1967) brought improvement to the field of electroenceph
alography, which at the time was faced with amplitude meas
urements of randomlike activity. Maybe more important yet,
it brought a consistent analysis technique, well established
from other areas with an enormous amount of computational
power. After the introduction of the Fast Fourier Trans
form (FFT) algorithm in 1965 by Cooley and Tukey, this
power increased manifold. At this point, however, the
means began to obscure the basic constraints of the method.
Let us review then the methods of spectral analysis.
One of the basic results is to obtain the power spectrum,
i.e., an estimate of the mean square value or average
intensity of the EEG as a function of frequency. It dis
plays the decomposition of the total variance into contri
bution from the individual frequency bands. To obtain the
power spectrum one can apply Fourier transform to correlo-
grams (indirect method, Blackman and Tukey, 1958), or take
directly the Fourier transform of the data and square its
absolute valueperiodograms (direct method, Dumermuth &
Keller, 1973; Matousek, 1973), or use autoregressive tech
niques (Gersch, 1970; Mathieu, 1970). After the introduction
of the FFT the direct method is by far the most widely used.


Fig. 32. Seizure for Patient #4. Period Slow Waves but Few Spikes.


302
TTTL C AL IS*
-*### Se:*-** ****::
* CALIBRATION
** it *** **** # ******* * *
*
*
*
*
2500
EVALUATES PEAK AMP.
OF CALIBRATION SIGNAL
AVERAGES OVER 64 PEAKS
AORG >2500
FF8 A
CALWSP
EQU
> FF S A
FC02 '
SPTHP
EOU
>FC 02
F CO 4
THRES
EQU
>FC04
0013
GA IN S
EQU
>1 3
0011
GA IN W
EQU
>1 1
1 EFO
ADC
EQU >1EFO
2 50 0
02E0
LVtfPI
CALWSP
2502
FF6A
2504
0206
LI
6 .ADC
2506
1EF0
250 8
0207
LI
7,>FFDF
250 A
FFOF
250C
C4C0
CLR
0
250 E
04C8
CLR
8
251 C
04E6
CLR
26 ( 6 )
2512
0006
2514
04E6
CLR
03(6 )
2516
00 08
25 18
020C
LI
12,>100
251 A
0 l 00
251C
1E00
332
0
25 I E
1D03
SBC
3
252 C
0300
LIM I
3
2522
0003
2524
0202
LI
2,3
2526
0003
2528
33C2
LDCR
2,15
2 52 A
1000
NOP
252 C
1 OFF
NEXT
JMP
$
2 52E
1000
NOP
2530
COCO
MOV
0,3.
2532
CO 26
MOV
a>E(6),0
RO RECEIVES DAT
2534
00 OE
2536
0280
Cl
0,0
2538
COOO
253 A
1 1F8
JLT
NEXT
POS I TI VE?
253C
80 CO
C
0 ,3
YES, >
PREVIOUS?
253E
1 501
JGT
POST V
REACH
PEAK?
2540
1 0F5
JMP
NEXT
NO GO
BACK
2542
1 OFF
POST V
JMP

2544
1000
NOP


230
were found in the present evaluation. Subsequently, only
3 < Sz < 10 shall be evaluated.
The proposed method also brings up the possibility of
making the wrong judgment. Probably a better idea is to
classify the seizures in categories: group one, most
probable detection; group two, less probable detection,
according to the proximity to the mean and variances of the
repetition period (or other parameters). The seizure clas
sification can also lead to the possibility of having dif
ferent algorithms analyzing the data. For instance, modi
fications in the seizure program could be made to allow for
the detection of periodic waveforms in the theta range
(slow waves) and avoid the relatively large number of
misses in the PM variant group. It would be convenient to
discriminate between the activity detected following one
rule or the other, not only for characterization purposes
but also to quantify detection performances (the simplified
rule would be more sensitive to artifacts).
All this discussion assumes that the statistics are
available, which may not be the case if the system is made
portable due to the large amount of memory required. An
alternate solution would be to start the data analysis with
a set of "cold start" parameters (the ones used in the dis
sertation) and dynamically adapt the parameters during the
session to fit the particular patient patterns. To mini
mize errors of false adaptation care must be taken: For
instance, require three seizures above a certain duration


21
the leading edge first derivative (negative excursion),
sharpness of the apex, and trailing edge first derivative
(positive excursion). The system requires fairly high
sampling rates and is somewhat sensitive to the amplitude
of the incoming signal and to muscle artifact, although in
a smaller degree than the systems that computed the second
derivative of the EEG.
Another detection scheme uses the amplitude-frequency
characteristics of the background activity and of the
spikes to define detection boundaries in a plane. It is a
modified scheme of the period amplitude-analysis of Leader
et al. (1967) and Carrie and Frost (1971). Ma et al.
(1977) used it to establish optimum decision boundaries
that turn out to be nonlinear to accommodate the dependence
of amplitude threshold with duration. It is necessary to
use each patient's background activity and an average value
taken from a population of subjects to estimate the bound
ary (assuming the clusters of normal and abnormal activity
are jointly Gaussian distribution with equal a priori
probabilities). The results seem promising but are depend
ent on the availability of the sets and are computationally
complicated and expensive (in time and memory dimensions).
Earner and Ostergen (1976) also used a similar approach
called sequential analysis to display the amplitude-
duration of the EEG but preserving the time information.
His methods show the clustering of paroxysmal spike
activity and some patterns as spike and wave. It is


Fig. 44a. Variance Repetition Period Versus Repetition Period (#5-1)


NOISE ANALYSIS NOi>L HUhlll.l- it, Uit-ftv&ill.-V 4Hi Ohul NV. BANDPASi
MAGNITUDE
-59. 86543
T. l)2 H "i. DI. i 1SI GW l-AV
-64. 66954.
If l11| h Ir i: H-
-69. 47366.
-74. 27779.
79.08191.
-83, 80603.
-88. 69016.
-93. 49420.
-9b 29840.
-3 03. 10251.
* *¡t
- 107. 90663.
**#**#**
in**-*****#*.
O. 10E-01 O 798 OI O. 1 &E 02 O. 24E 02 O. 32E 02 O 40E 02
O. 4OE O i O 120 02 0.202 02 O. 28G 02 O. 36E 02
FREQUENCY (HTZ)
tr *= o. 30E-03 volts
FREQUENCY ANALYSIS NODE NUMBER 16
Fig. 9b. Filter Noise Analysis Using DINAP
00


< 10 sec and Sz > 10 sec is taken into consideration, the
agreement decreased to 77 percent.
Besides outputting the information about number of
seizures, their duration and time of occurrence, the detec
tor also presents a detailed analysis of the detection
parameters. These results, the first of their kind ever
reported, include the mean and variance for the PM recruit
ing period, the half period of the slow waves, the delay
between the slow wave and the spike, and the amplitude of
the filtered spike and slow wave. They show the constancy
of the period measures inter and intra seizures for the
same patient and the higher variability of the amplitude
measures.
Preliminary results correlating pairs of the detection
parameters are also presented for three patients. The
automated detection and quantification of PM seizures,
using the present system, are critically brought to a
focus.
viii


TABLE II
DIGITAL FILTER CHARACTERISTICS
Filter
Quadratic
Factors
Attenuation
Characteristics
(Ilz)
Magnification
Noise
a^ /a ^
out in
Combination
Chosen
k
-12
-3
3
-12
-24 dB
Best
Worst
Best Worst
id Design
Slow
Wave
C, = l.6404
D7=-.8250
C^I.8064
D2=-.8250
(1A3F)
(D334)
(1CE7)
(D334) jj
0.3
0.8
6.0
8.2
11.6
68
113
960
4400
C],Dj_# +1
Co*D2, 1
Gain 68
Noise 1200
3.80
id
A
1
£
0
U
u
nj
a
Spike
Cj =1.5832
D,=-.8684
C2=l.7761
D2=-.8684
(1955),,
(DE52)
(1C6B)
(DE52)
6.5
10.2
23.0
26.8
34.8
78
. 84
900
10000
ci.iv+i
C216911
Gain 78
Noise 1100
5.50
G
tT'
H
10
Q
'
Slow
Wave
Ci=1.5287
Di=-.7435
C2=l.8939
D2=-.9155
(1876),,
(BK53)
(1E4D)
(EA5C)
0.3
0.9
7.2
10.8
18.4
18
118
580
3600
C]_' Di, +1,-1
C51^2f"1
Gain 18
Noise 630
0.51
G
A
1
a
IS
Spike
Ci=l.5404
Di=-.8349
C2=l.8041
D2=-.9033
(18A6)
(D5BF)
(1CDD)
(E730)
4.0
9.2
24.0
30.0
45.6
33
98
210
1900
C1,D1,+l,-l
c2, d2 >-i
Gain 33
Noise 290
3.70
117


84
addition is performed, the addends must be aligned. If the
filter computations are correct, the part of the product
retained must be aligned with the input; otherwise, the
additions which involve the input will not yield the cor
rect result. Hence, the least significant bit of the part
of the produce retained has the same weight of the input,
even when the computation wordlength is bigger than the
input number of bits. The alternate argument follows the
"binary point" across the various shifting operations to
yield the correct alignment. This will be explained in
Appendix II.
To evaluate the total noise at the filter output, the
roundoff noise power produced by each source will be added
to the input quantization noise, since it is assumed that
the noise sources are uncorrelated. There are three quan
tities that are important noise parameters: the peak in-
band noise referred to 1 volt, the A/D converter precision,
2 2
and a dimensionless number a ,/a. which is a measure of
out m
the noise gain of the system and may be translated into the
number of bits of the output that are "noisy" (one bit cor-
2 2
responds to powers of a ./a. = 3.98). From this ratio
c out in
and the square of the filter midband gain G the noise fac
tor K
2 2
a ./a.
out m
K
(47)


Microcomputer System
Pig. 22. TI 9900 Microcomputer Block Diagram
138


TABLE VIIcontinued
PATIENT #7
Session
(EEG Mon
tage)
Repetition
Period (sec)
Half Period
Slow Waves
(sec)
Delay Slow
Wave Spike
(sec)
Filtered
Slow Wave
Amplitude
(yV)
Filtered
Spike
Amplitude
(yv)
In Sz
In
X
a
X
a
X
a
X
a
X
a
SessiorT"\^
\ 0.07
Y 0.02
Y 0.23
Y 7-16
Y 8.40
1st
0.32
\
0.11
0.13
V
146
152
Y
W

q.oA.
O.oV
0.39 y
11.80V
I3.3V
Yo.08
Y 0.03
Y 0.34
Y 6.69
YlO.90
2nd
0.33
Y
0.11
0.13
130
153
\
(Fz-a2)
0.12Y
0.0V
0.3s\
13.oV
20.7\
Y 0.10
\ 0.03
\ 0.42
\ 8.54
\ 8.70
3rd
0.35
Y
0.12
0.13
\
144
\
134
Y
(F -0 )
\
\
\
\
3 z
0.09Y
0.03\
0.16 Y
11.70\
9.66Y


263
0001
TITL
INTHAND*
0002
*-
INTERRUPT HANDLER
0003
*
PERFORMS THE TIMING FOR THE A/D CONVERSION
'0004

LOAD THROUGH THE MONITOR IN FF88 B @2200
0005
ft
FF88=0460
0006

FF8A=2200
0007

IF THE
BOARD IS TM
990/100
0008
ft
0009
2200
AORG >2200
0010
2200
0201
LI
1,>1EF0
2202
1EF0
0011
2204
C842
MOV
2,@>A(1)
INITIATE CONVERTION
2206
OOOA
4
0012
2208
02QC
LI
12,100
SET CRU ADDR TO 9901
220A
0064
0013
220C
0201
LI
1,>495
INT EVERY 12.5 MS
22CE
0495
0014
2210
33C1
LDCR
1,15
0015
2212
1EQ0-
SBZ
0
0016
2214
1D03
SBO
3
0017
2216
0300
LIMI
3
2218
0003
0018
221A
05CE
INCT
14
LEAVE WAIT LOOP
0019
221C
0380
RTVP
0020
END
*0000* NO.OF ERRORS IN THIS ASSEMBLYs 0000
NO. CF RELOCATABLE LOCATIONS USED = 0000
# OF-OBJECT RECORDS OUTPUT* 3
END OF ASSEMBLY
£ED


146
CODE
A/D CONVERTER
FILTER
INTHAND
MAIN
PEAK
SPIKE
CALIB
STATIS
SZURE
1EFO
FCE2
1EFE
2000
FD00
FD02
2158
FD20
2200
FD3E
FD40
2226
2240
FD60
2332
FD80
23C0
FDA0
2480
2499
FDC0
24FE
FDE0
2500
FE00
2582
2590
FE20
25F4
FE40
2600
FFAA
26F6
FFCA
WORK SPACES
FIRST (FILTER)
SECOND (FILTER)
THIRD (FILTER
FOURTH (FILTER)
WPIKE
WMAIN
WSTAT1
WSTAT2
WSTAT3
WSTAT4
WSTAT5
INTERRUPT III
WCALIB
Fig. 26. PM Detector Memory Mapping


98
1
J
3
(
l

k
r,
V
IV-
...
IV-
... u .
IV
: n
M
IV
n
j*\
n
i / V:
1 l
: J
r: j
a; ; :
: :
n
/
V
I
: /A
f\ :
i i
: !
\
i
: 1

i l
} :
7
\ i
\
i
i
: /
t
\
: f :
r\ :
} :vs
1
: i
\
i
: I
1
:| :
: \7.
t : :v-v7|
: 1
V
i
i i
A 1
I
ii ;
. i 11
i i i
¡ J
1
!
\,4
! I
w
s \
1
l :
! II
1
'1
1
: l
V
i1
.7 :
i 1
1
: -II
:
j
: i
11
1 I :
: : l
!
: = : I
: l
i 1
: 1
i i
1 ¡
: 1
: : 1 t
' 1=
1 1
i 1
IF
; 1 i
: : II
1 f
i : 1 f
C
11
i (
II
3 1 :
: Ml
1
: : M|
I-
11
: 1
U
) |: :
: i 11
1
: : Ml
i i;
tr
If
1 l'4'-:'
? Ml
MM
f f i"
'i i
II
1 |
- r ¡1
1 /
Mi
l l
u
I
U
\J: :
: u
1 J
: 1
1 f :
u
I r
l
'
: : J
\l
: M
V :
\
V
1
; ; i
F
f 1
I:

0.3 sec
1 First Spike
2 Second Spike
3 Slow Wave
4 Positive Transient
Fig. 10. Spike-Wave Complex (Patient #7) Digitized
100 Hz


AUTOMATED DETECTION AND QUANTIFICATION
OF PETIT MAL SEIZURES IN THE ELECTROENCEPHALOGRAM
BY
JOSE CARLOS SANTOS CARVALHO PRINCIPE
A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
1979


298
2 0C4
OA 17
POST 2
SLA
7 1
20C6
A 1C9
POSTS
A
9,7
20C8
C003
MOV
3,0
2 OCA
0820
SR A
0 ,2
20CC
04CC
CLR
12
*
CALCULATION OF ;
4
RECURS ION RELAT
4
XI+=0X2+E+C(XI
4
X2+ = X1
E
4
Y=X2
4
REG USED
4
R16 FUR
E
4
R7 FOR
XI
4
R3 FOR
X2
2 CCE
02E0

LWPI
FIRST
20D0
FCE2
2 002
0743
A6S
3
200 4
38C2
MPY
2 ,3
20 06
1101
JLT
P0ST3
2 00 8
0503
NEG
3
200A
AOCF
POST 3
A
15,3
20DC
C243
.
MOV
3, 9
200E
61CF
S
15 ,7
20E0
C0C7
MOV
7,3
2 0E2
0747
A8S
7
20E 4
390
MPY
1 ,7
20E6
1503
JGT
PQST9
2 0E8
0 A 17
SLA
7,1
2 OEA
0507
NEG
7
20EC
1501
JGT
P0ST4
2 0EE
0 A1 7
POST 5
SLA
7,1
2 OF 0
A 1C9
POST 4
A
9,7
20F2
0 43
MOV
3,5
2 OF 4
0835
SRA
5,3
20F6
C345
MOV
5,13
4
A
IMPLEMENT SPIKE
2 OF 8
02E0
SLOW
LWPI
THIRD
20FA
FD 20
20 FC
0 66
MOV
2>E(6),5
20FE
0 0 OE
2100
08 15
SRA
5, 1
2102
0743
A8S
3
2104
3 8C2
MPY
2,3
2 1 ce
1101
JLT
P0ST6
2108
05 03
NEG
3
210A
A 0C5
POST 6
A
5,3
210 C
C243
MOV
3,9
21 OE
A 1 C5
A
5.7
2110
C0C7
MOV
7,3
2112
0747
A8S
7
CC X1+EJ-DX2+E IN FT7
XFER YN TO 2ND RESONATOR
SCALE SIGNAL
2ND RESONATOR
^ IS
GAIN 1M



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PAGE 301

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&O 6=0,1 ,1& 5(63(&7,9( 6= &2817 -*7 &2 17 $ $ , 1& /(6 6= & )&$ ( -03 &87 $ &2 17 &O 7(1 $ $ -*7 DL* $ $ ,1& /(6 6= $ )&& $ $ -03 67$ $& $& %,* ,1& *57 =! $( )&( 5($'< )25 727$/6 $ 67$ ,1& ž)/$* )& /:3 67$7 55$7( )&2( & r 029 67 $7, $ )&2( 6& &)$' 029 f r 0($1 ( & &)$2 029 fr 9$5,$0&( & 3(5,2' 2) 6: & %/:3 67$7 & )& & & 029 67$7 &$ )& && &)$' 029 e f } &( &)$2 029 f 2/:3 67$7 '(/$< 63,.( 6: )& & 029 67$7 $ )& '& &)$2 029 f '( ) &)$' 029 f ( 6: $03/,78'( F( %/:3 67$7 ( )& ,$ ( & 029 67$7 ( $ )& $ (& &)$2 029 f (( ) &)$' ! D \ f ) 63,.( $03/,78'( ) / :3 D67$7 ) )& ,( ) & 029 67$7 )$ )& ,( )& &)$' 029 f )( & &)$' 029 f &87 /, !)))) 287387 6(3$5$7,21 7$* )))) &) 029 $ &( 029 D6=7,0 6725( 0(0 32,17(5 & )& ( (2 &/3 )/$* 12 727$/6 )25 67$7,6 )& &) 029 7+5( 6 5(6725( 6: $03 7+5(6 ) & & % 6=&87 *2 72 0$,1 (1'

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PAGE 305

r r 6(7 83 2) 706 $6 $ 7,0(5 2& /, ! 5 +$6 $''5 2) $ (22 6%= (1$%/( ,17(55837 & 6 35,25,7< 6(7 72 ( /,0, 6(7 ,17 0$6. & /, )25 ,00(',$7( ,17 & r /'&5 )) A -03 $ 1&3 :$,7 )25 ,17(55837 & ( /:3, 6(&1' ( )'22 %$&. /, 0$6. ))) 6=& D!&^f (1' 2) &219(56,21" RRRF ) -(4 %$&. 12-803 %$&. &$ RV HF ,1& 6.,3 72 6(7 += & & &O &( &$2 -/7 6/2: $ &$ 029 D!(f}O2 5,25(&(,9(6 '$7$ 32,17 $ 222( $ RDL$ 65 $ 6&$/( ,1387 r &$/&8/$7,21 2) 67 5(621$725 r 7+( 5(&856,21 5(/$7,21 ,6 ; ';e&;O(f ; ;O ( r \ [ r 5(*,67(5 86(' ‘r 5(*,67(5 )25 ,1387 ( r 5(*,67(5 )25 ;, r 5(*,67(5 )25 ; $ $%6 *(7 6,*1 2) < $$ & 037 f§'; ,1 5 5 $& -/7 3267 -803 ,) 3 3&6 $( 1(* ,) 1(* &203/ 5 $ 2&$ 3267 $ ';( ,1 5 & 029 6$9( ,7 ,1 5 $&$ $ ;O( ,1 5 && 029 ;O( ,1 5 $%6 $ & 03< & -*7 3267 %( $ 6/$ $//,*1 %,1$5< 32,17 & 1(* & -03 32676

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PAGE 307

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PAGE 310

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PAGE 311

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PAGE 313

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PAGE 314

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PAGE 355

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PAGE 356

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Fig. 31. PM Seizure (Patient #5)
172


213


116
completely unacceptable for fs=240 Hz. It was decided to
reduce the sampling frequency to decrease the Q of the fil
ter. Using (48), and requiring a precision of 0.3 Hz
(10 percent) in the period measurements, a sampling fre
quency of at least 80 Hz is necessary. The closest integer
decimation ratio is 3, and so a sampling frequency of 80 Hz
was selected for the slow wave channel. With this sampling
frequency for the slow wave channel, the input data must be
properly lowpass filtered to avoid aliasing. As the fre
quency range of interest is 2-5 Hz, the first frequency
band that is aliased back to this range is 75 to 85 Hz.
An analog lowpass filter with cut-off at 25 Hz, 18 dB/oct
was utilized, yielding an attenuation of 54 dB in the above
frequency range. This number is thought sufficient not to
degrade the performance of the detector.
As it is indicated in Peled (1976), the FIR filters
are preferable to HR implementations from the computation
time point of view for decimation ratios greater than 5 for
fourth order filters. Therefore, the IIR design was also
used for the slow wave bandpass filter. Table IT presents
the filter's characteristics as obtained with the DINAP
program and the program described in Appendix I. Following
the design criteria outlined in Chapter II, the best pairing
and cascading were obtained and are shown in Table II,
along with the output noise variance and K.
The narrow- and wide-band design were utilized to
study the filters. The magnification and attenuation


241
Tn+1(w) = 2wTn(w)-Tn-1(w)
T2(w) = i[T (w)+l] .
n zn
(1-3)
By straight forward substitution of cos
x 2 2
e = cos hx+sm hx, sm h = cos h x-1,
obtain
hx =
x, -x
e +e
it is possible to
T (w) = (w-h/w2-^) n+ (w+42-1) ~n
n 2
T (w) = (w-i/w2-!) n+ (w- Jw2-I) ~n
n' 2
(1-4)
which are valid for w>l and w Some properties of the set are the following:
1) For n even or odd the polynomials are even or odd
functions of w.
2) Every coefficient is an integer, and the coeffi-
n_ ^
cient of highest degree term is 2
3) For n even the absolute value of each polynomial is
unit for w=0 and w=l.
4) In the range -1 equal ripple property, varying in amplitude between
1 and -1.
5) The total number of valleys and peaks for positive
w is n.
6) At the edge of the passband, the magnitude goes
through a minimum.


Power (Arbitrary Units)
#
Fig. 13. EEG, Muscle and Aliased Muscle Frequency Ranges
113


317


102
spikes are sporadic or substituted by polyspikes. Fig. 11
presents some examples. From an analysis of the data it
was concluded that these patterns appeared with enough fre
quency to be taken into consideration. The information of
the spike is included to differentiate PM patterns from
slow wave sleep, where 3 delta or theta waves may occasion
ally appear with the 3 Hz repetition rate.
After entering a PM paroxysm it was decided to require
only the existence of slow waves with the prescribed repe
tition rate. In this way the detection scheme will be
transparent to irregularities of the spikes. Another point
is the fading of the patterns in the middle of the ictal
event. When the slow wave pattern becomes irregular for
less than one second (either from a frequency point of view
or even the absence of slow waves) and restarts again, the
scorer generally calls the whole event one PM seizure.
This scoring methodology was incorporated in the detection
scheme: First the slow wave threshold was lowered 3/4 to
account for possible fading, and a "hysteresis" of one
second was allowed before ending the seizure count.
It is felt that the criteria as enunciated will not be
very tight, which means that the performance may be biased
towards the false positives, i.e., nonseizure activity
scored as abnormal. The criteria could easily be biased on
the opposite direction, but it is felt that when analyzing
data from PM patients, it is more costly to miss abnormal
activity (mainly in a drug study) than tolerate a small


304


TABLE IVcontinued
PATIENT #12
Human
Computer
1 < Sz < 3 sec
3 < Sz <10 sec
Sz > 10 sec
Agreement in
Seizure Detection
(# of Sz)
15
13
33
33
0
0
Agreement in
Seizure Duration
(# of Sz)
12
30

Total Time in
Agreement (sec)
221.3
205.1
0
20.8
Computer Counts
30
35
2
Computer Misses
2
0
0
Computer False
Detects
17
2
0
180


243
which is equivalent to
(2k+l)7T
2n
cj) = sin h-1
2 n e
k=0,1,2, ... n-1
(1-9)
The left half plane poles (7) are
Sv = sin h0 sin + j cos hcf,, cos
(2k+l)TT
2n
k=0,1,2, ... n-1
where (Weinberg, 1962)
sin h(j>2 =
cos h4>2 =
l/F**;)'
y + 1 +
e
_1
1, n
(1-10)
To determine n, the polynomial order, from the attenuation
in dB/octave, (4) can be approximated by
T s ('
n 2
I 2 n
w+v W -l"!
for large n. Therefore,
log (2Tn(w))
n = 1
log
(w+i w^-
(1-11)
1)


168
NA .ME: SUBJECT =:
TAPE *: START FOOT. : END FOOT. :
MONTAGE:
FRONT
TOP OF HEAD
ELECTRODES:
cup/disc
needles
OTHER:
P4STE:
grass
bentonite
collodion
OTHER:
ADDITIONAL:
Fig. 30continued


12
for this more general case (Treitel et al., 1977). How
ever, as an infinite AR process can approximate any ARMA
process, this property of the AR model is preferred. The
FPE criteria to determine the order of the AR model can
still be used, but there is a tendency to overestimate the
order (Ulrich & Bishop, 1975).
After briefly reviewing the three approximation models
(MA, AR, ARMA) to estimate the power spectrum, a question
must still be answered. From the sequence of the random
process available how should one decide what model to use?
This question (identification problem) has not yet been~
answered in general, and only in some cases the physical
knowledge of the generation process of the data has helped.
It is surprising that we have not seen published any work
in this direction by the users of these techniques in EEG.
On the contrary, the approximation properties of the AR
model have been exclusively used. There are reports in the
literature (Treitel et al., 1977) that clearly show that
this can lead to inappropriate approximations, which means
that there is no single correct technique to calculate the
spectrum in the absence of knowledge about the physics of
generation.
In EEG the autoregressive model has been used by Fen
wick et al. (1969) to predict evoked responses. Pfurt-
scheller and Haring (1972) used AR models to attempt data
compression. Gersch & Sharp (1973) used AR models for
multivariate EEG analysis. Wennberg & Zetterberg (1971)


52
order to meet the specifications and gives the values of
the S plane bandpass filter poles, the z domain filter
poles and the quadratic factors C and D for each second
order resonator given by (a cascade implementation is
assumed)
C = 21^ (z)
(14)
The number of zeros at each of the points (z=l) is
printed. The frequency response of the filter is also
plotted for a quick check on the design.
The above procedures design infinite impulse response
(HR) filters. For EEG applications, where the attenuation
characteristics seem to be more important than the linear
phase characteristics, the IIR seem to be preferable to the
finite impulse response filters (FIR). However, it is
worth mentioning that the FIR can be designed to present a
linear phase across the passband, which may be important
for applications where the phase information of the input
will be an important parameter. Another application which
may call for FIR is the situation where multi-sampling
rates will be used.
One of the great problems in digital filter design, as
mentioned earlier, is the lack of independent midband gain
control. Therefore, when a narrow-band filter needs to be
designed, the gain shall be expected to be high. To


2222
QA 84
C
4 3> 12 ( 1 0>
2224
00 12
2226
16F9
J NE
BAQ
2228
0380
RTWP
222 A
C100
MOV
0. 4
NORMALIZE X FOR DISPLAY
222C
3 91A
MPY
*1 0 .4
222E
3001
DIV
1 *4
223 0
A12A
A
a>io (io J *4
ADD X TO XO
2222
0010
2234
0205
LI
5,3
TYPE OD PLOT
223 6
0003
2233
2 1 6A
C
3>14(10) ,5
2 23 A
00 14
223C
1336
JEQ
LINE
223E
0205
LI
5,2
2240
0002
2242
S16A
C
3>l4(10),5
224 4
0014
2246
1 30F
JEQ
STEP
*
POINT
PLOT
2248
C644
MOV
4 *9
224 A
C 102
MOV
2,4
NORMALIZE Y
224C
391 A
MPY
*10,4
224E
30 03
DIV
3,4
2250
A1 2 A
A
3>10(10),4
ADD YO TO Y
2252
0010
2254
C16A
MOV
a> l 0(10) ,5
DRAW LINE FROM X AXIS
2256
0010
2256
0535
AGA I N
INC
5
TO Y
225 A
CA45
MOV
5,32(9)
225C
0002
22SE
C69C
E3L
*12
226 0
8 1C5
C
5,4
2262
i 6F A
JNE
AGAIN
2264
0380
RTWP
*
HYSTGGRAM
2266
C66 A
STEP
MOV
22 < 10),*9
OUTPUT X.Y
2263
00 02
226 A
CA6A
MOV
24( 10) ,32(9)
2 26C
0004
226E
0 0 02
2270
C69C
BL
*12
2272
OS AA
INC
32(10)
INC OLD X
2274
0 0 02
2276
8 12A
C
22( 10) ,4
ARRIVE AT NEXT PGINT?
2273
0 0 02
227A
1 6F5
JNE
STEP
227 C
C 1 02
MOV
2.4
NORMALIZE NEW Y
227E
39 1A
MPY
*10,4
2280
3D 03
DI V
3,4


260
0055
0001
TITL
'CHE3Y
0056
0002
*
0057
0003
ft
2ND ORDER CHEB7SHEV DIGITAL FILTER PRCGRi
0053
0004
ft
0059
0005
ft
CHARACCTERISTICS
0060
0006
ft
BANDPASS 7 TO L7 HZ
C061
0007
ft
RIPPLE 20
0062
0008
ft
ATTENUATION 12 DB/OCT
0063
0009
ft
SAMPLING FREQ 30 HZ
0064
0010
ft
0065
0011
ft
INITIALIZATIOS
C066
0012
ft
0067
0013
2130
AORG
>2130
0068
0014
20E2
FIRST
EQU
>2CE 2
0069
0015
2100
SECSD
EQU
>2100
0070
0016
1EFE
INPUT
EQU
>1EFE
OUTPUT CF A/D
0071
0017
1EF2
OUTPT
EQU
>1EF2
D/A CONVERTER
0072
0018
1EF0
ADC
ECU
>1EFC
0073
0019
7FFF
MASK
EQU
>7FFF
0074
0020
3417
Cl
EQU
>3417
FILTER CCEF IN HEX
0075
0021
B9C7
D1
EQU
>B9C7
CC76
0022
1623
C2
EQU
>1623
0077
0023
B9C7
D2
EQU
>B9C7
0078
0024
ft
0079
0025
2130 02EC
LWPI
SECND
DEFINE 2ND WORKSPACE
0080
2132 21CC
0081
0026
2134 0201
LI
1,C2
R1 GETS C2
CCS2
2136 1628
0083
0027
2138 0202
LI
2,C2
R2 GETS D2
C084
213A 1628
0085
0028
213C C4C3
CLR
3
CC86
0029
213E 04C4
CLR
4
0037
0030
2140 04C7
CLR
7
0088
0031
2142 C4C8
CLR
8
0089
0032
2144 0203
LI
11,INPUT
R11 HAS ADDR CF INPUT
0090
2146 1EFE
CC91
0033
*
0092
0034
2148 O2E0
LWPI
FIRST
DEFINE 1ST WORKSPACE
0093
214A 2CE2
0094
0035
2140 0201
LI
1 ,CT
R1 GETS Cl
0095
214E 8417
0096
0036
2150 0202
LI
2,D1
R2 GETS D1
0097
2152 B9C7
0098
0037
2154 C4C3
CLR
3
0099
0038
2156 C4C4
CLR
4
0100
0039
2158 04C7
CLR
7
0101
0040
215A C4C8
CLR
8
0102
0041
215C C20D
LI
13,OUTPT
R13 HAS ADDR CF 'OUTPUT
0103
215E 1EF2
0104
0042
ft
0105
CHEBY
PACE
0106
RECD
LOC CBJ
SOURCE STATEMENT
0107
0043
ft
SET UP OF A/D CONVERTER
0108
0044
ft
ANALOG DEVICES RTI-1241
0109
0045
ft


TABLE OF CONTENTS
Page
ACKNOWLEDGEMENTS ii
ABSTRACT vi
CHAPTER
ILITERATURE SURVEY . 1
Spectral Analysis 1
Time Domain Approach 18
Selection of the Method of Seizure
Detection 25
IIMICROCOMPUTER BASED DIGITAL FILTER DESIGN . 30
Preliminary Considerations 30
Design Criteria 35
Filter Transfer Function . 38
Lowpass to Bandpass Transformations 41
Transformations to the Z Plane 43
Finite Length Effects of the
Implementation 53
Practical Considerations 84
IIIA MODEL FOR PETIT MAL SEIZURES AND ITS
IMPLEMENTATION 94
Detection Problem 94
A Petit Mai Seizure Model 98
Definition of the Implementation Scheme ... 106
System Implementation 136
Testing of the Program 157
IVSYSTEM EVALUATION AND PRESENTATION OF
RESULTS 165
Description of Data Collection 165
System Evaluation .... 170
Statistics of Seizure Data 187
Analysis of the False Detections and
Proposed Improvement in the Detector ... 224
Proposed System Utilization and Concluding
Remarks 233
iv


67
(zero at z=-l). This fact has been experimentally noticed
in (Mick, 1975). It may also give a."rule of thumb" for
the pairing of zeros and poles in the feedforward struc
ture: the zero closer to filter passband shall be imple
mented first for reduced magnification. The goal is to
bound the maximum magnification by the input-output filter
gain. When this is possible, both structures present the
same wordlength requirements. However, they may display
quite different noise power at the output. Fig's. 5a and b
present the structures for fourth order filters designed
with the direct substitution, narrow-band, wide-band, and
the feedforward implementation. The implementation with
the canonic form is pictured in Fig. 5c.
Noise Analysis
The effect of truncation (rounding) is apparent in
three main areas: the A/D conversion, the multiplications,
and the coefficient quantization. As the phenomenon has
the same basic characteristics, its modelling will be over
viewed first.
Quantization is a nonlinear operation on the signals,
but can be modelled, as a superposition on the signal of a
set of noise samples shown in Fig. 6 (Rabiner & Gold,
1975). The quantized samples will be expressed by
x(n) = Q[x(n)] = x(n)+e(n) (31)
where x(n) is the exact sample and e(n) the quantization


81
higher than the Nyquist rate. Also, the implementation of
bandpass filters with low center frequencies are the ones
which are most sensitive to quantization effects and so
should be the ones closely monitored. Practically this can
be accomplished by checking the frequency response of the
filters obtained with the truncated coefficient values to
see if they meet the .design specifications. ,
A/D conversion noise. The A/D conversion noise is the
uncertainty derived from the use of finite precision to
represent the analog signals. The assumption of independ
ent signal and noise allows one to proceed with the noise
computations while ignoring the signal. Let h(nT) be the
system impulse response and H(z) the corresponding transfer
function. Then the output autocorrelation function Ry(nT)
for the noise e(nT) is
00
Rv(k) = l y(n-k)y (n)
* n=0
CO
00
00
l l h(p)e(n-k-p) £ h(m)e(n-m)
n=0 p=0
m=0
~ 1 1 h(p)h(m)Rx(k-m-p) .
(43)
p m
The variance is obtained for k=0; therefore
aj = R (0) = l l hipJMitORxim-p)
Y Y rS m
p m
(44)


296
*
201 A
02E0
LWPI
THIRD
20 1C
FD 20
201 E
0 201
LI
1C3
2020
E355
2022
0202
LI
2 >03
202 A
DE52
2026
04C3
CLR
3
2028
0 4C4
CLR
4
2 02 A
04C7
CLR
7
2 02C
04C8
CLR
8
202 E
04C3
CLR
11
2 03 0
0206
LI
6, ADC
2 03 2
1EF0
*
2034
0 2E0
LWPI
FORTH
2036
F03E
2038
0201
LI
1 C4
203 A
CAA8
203C
0202
LI
2 D4
203E
DE 52
2040
0 4C3
CLR
3
2 042
04C4
CLR
4
2 044
04C7
CLR
7
2046
04C8
CLR
8
2048
0206
LI
6 ADC
20 4 A
1EF0
2 04C
02E0
LHP I
FIRST
DEFINE 1ST WORKSPACE
204E
FCE2
2 05 0
0201
LI
1 ,C1
R1 GETS Cl
2052
E739
2054
0202
LI
2,0 1
R 2 GETS D1
2 056
0334
2053
04C3
CLR
3
205 A
0 4C4
CLR
4
2 05C
04C7
CLP.
7
205E
04C8
CLR
a
2 06 0
0200
LI
13,0 UT 2
R13 HAS ADDR OF OUTPUT
2062
FD 84
*

SET UP
OF A^D
CONVERTER

ANALOG
DEVICES
RTT-1241
2 064
02 05
T
LI
5 >FF68
2066
FF 68
2068
04D5
CLR
#5
206A
0206
LI
6 ADC
206C
1EF0
206E
04 E6
CLR
a>6{6)
SET GAIN TO 111
2070
0 006
2072
04E6
CLR
3>3(6)
DISABLE AUTO INC MODE
2074
0008


186
evaluated. The most bothersome feature is the appearance
of false detections, which will be closely analyzed in one
of the next sessions. The computer misses plus false
detections decreased the agreement in detections to 82 per
cent for 3 < Sz < 10, while the agreement in detection for
Sz > 10 sec is still a high 92 percent, with an average of
86 percent for Sz > 3 sec. It can be concluded that the
system, as it was evaluated, is able to present a good pic
ture of the occurrence of clinical significant seizures in
the EEG of unrestrained patients.
In the three recordings analyzed, one was obtained
after the Depakene treatment. The neurologists evaluated
the drug usefulness, so a similar procedure was undertaken
with the outputs available, i.e., the detector outputs for
each session and the corresponding human scoring.
Two remarks need to be made before explaining Table VI.
First, the conclusions from the usefulness of the drug can
not be taken from this table, since the patients were, on
purpose, selected to show a high number of seizures in
every session, because the goal was to test the detector
with seizure data. The drug is reported to be very effec
tive overall with the 25 patient population (Wilder et al.,
1978). Second, only a fraction of the total session time
was analyzed (the number of hours is shown in brackets),
therefore, the discrepancy between these and other published
results.


analysis method (plotting of variables) was thought ade
quate for the analysis instead of statistical analysis
techniques.
A program that gets the data (DATA) according to the
data format and another that plots it using a Tektronix ;
611 storage display (PLOT) were written for the TI 9900
microcomputer. They are presented in Appendix III.
The analysis applies to the classical PM patients
(#5, 7, and 12) unless explicitly stated otherwise. The
first pair of variables plotted was the seizure duration
versus the time of occurrence (X axis). Ultradian char
acteristics of the seizure activity were sought. The
reported (Stevens et al., 1971) 80-120 minutes inter-ictal
period was not observed, but there were a lot of external
conditions that could have disturbed the observations
(small period of observation6 hours, hospital environ
ment) The tendency for the paroxysms to appear in clus
ters (one big surrounded by smaller ones) was noticed in
patient #5 (Figs. 33a and b). Patient #12 also displayed
this characteristic in the first session, but after the
drug it disappeared (Fig. 34). Patient #4 displayed an
interesting change of seizure characteristics from awake to
sleeping conditions. In the awake state he presented long
spaced seizures, but when asleep (early stages, STl, ST2)
the seizures were much closer and of smaller duration
(Fig. 35). The seizure period parameters remained fairly
constant with the time of the day, and a higher variability


324


66
Fig. 4b. Feedforward Structure


TABLE IVcontinued
PATIENT #5
Human
Computer
1 < Sz < 3 sec
3 < Sz < 10 sec
Sz > 10 sec
Agreement in
Seizure Detection
(# of Sz)
88
57
37
34
21
21
Agreement in
Seizure Duration
(# of Sz)
46
29
18
Total Time in
Agreement (sec)
190.5
180
332.2
316.4
Computer Counts
90
41
20
Computer Misses
31
3

Computer False
Detects
39
4
0
178


300


False
Detection
07 sec 1.46 sec


269
2288
FD60
2 2B A
0206
LI
6 SPI KE
PC FOR SPIKE
2 25C
2490
223E
0207
LI
7 WINPT
WSP FOR FILTER
22C0
FD3E
22C2
0208
LI
8.INPUT
PC FOR FILTER
2 2C4
2000
22C6
0407
3LWP
7
GET 1ST POINT
22C8
C002
MOV
2,0
STORE IT IN RO
2 2CA
4020
SZC
2MASK,0
TAKE SIGN
22CC
FC06
22CE
02E0
lwpi
I NT VIP
SET WSP FOR INT 3
22C0
FF8A
22D2
04 C9
CLR
9
CLEAR SECONDS CLOCK
2 2D 4
02 OA
LI
1 0 >F0
COUNT SEC
2206
00 FO
2208
02E0
LW PI
WPIKE
SET WSP FOR SPIKE
2 2D A
FD 60
22DC
CO 03
MOV
3,0
GET 1ST POINT
2 2DE
4020
SZC
DMASX,0
TAKE SIGN
2 2E0
FC06
A,
*
FUNCTIONAL LOOP
22E2
02 EO
LWP I
MAIN
2 2E4
FOSO
2 2E6
04 Cl
AGAIN
CLR
1
CLEAR R.RATE COUNTER
22E8
06A0
BL
SPEAK
GET NEXT PEAK
2 2EA
23A 0
225C
0281
Cl
1 HP. ATE
WITHIN LIMITS?
22E5
00 SO
2 2F0
15FA
JOT
AG AI N
NO GO 3ACK
22F2
C 281
Cl
1 LRATE
2 2F4
0 034
22F6
l 1F7
JLT
AGAIN
22F8
0201
LI
1,HRATS
2 2F A
0080
22FC
06 AO
AGAINI
BL
SPEAK
GET NEXT PEAK
2 2FE
23 AO
2 20 C
0281
Cl
1 HHRAT
WITHIN LIMITS?
2302
0100
2304
15F0
JGT
AGAIN
NO GO BACK
2306
C 2 81
Cl
1 LL.RAT
2308
0084
2 30 A
1 1 ED
JLT
AGAIN
230 C
0201
L I
1 .COUNT
RI HAS MAX ALLOWABLE DELAY
2 20 £
0 120
221 C
8301
C
1 SDELAY
DID SPIKE OCCUR?
2212
FCOO
2314
15 03
JGT
EV ENT
YES SZ RECOGNIZED
2316
0201
LI
1 ,HRATE
SEE IF SPIKE OCCUR DUPING NEXT
2318
0 0 30
231 A
1 OF 0
JMP
AGAIN1
2 3 1C
020C
EVE N T
LI
12 ,>7FF
10 V IN D/A
231 E
07FF
232 0
CSOC
MOV
12 3ADC
2322
1EF0
2324
0460
3
SSZURE
GC TO SZUP.E
2326
2620
2228
020C
SZCUT
LI
12,>300
-10 V IN 0/A
232 A
0800
232C
C 8 OC
MOV
12,S ADC
232 E
1EF0
2330
1000
NOP
2232
10D9
JMP
AGAIN
RESTART SEARCH
END
)* NOOF ERRORS IN THIS A SSE M3LY = 0000
:f relocatable locations usec = oooo


233
to implement). At the same time the impulse response
characteristics of such filters will be evaluated and com
pared to the "classical" bandpass design.
Proposed System Utilization
and Concluding Remarks
One of the characteristics of abnormal EEG studies is
the generation of huge quantities of data which have to be
analyzed carefully to distinguish the abnormal patterns.
It will be very difficult with automated systems to match
the pattern recognition ability of the human scorer. How
ever, as long as the agreement automated system/human is
fair, the automated system can be used with advantages:
first, the criteria are not subject to change with learning
experience or data context resulting in a better objectiv
ity; second, the automated system has available the param
eters used for the detection and therefore can produce much
more detailed information about the data analyzed than the
human; third, it can perform a substantial data reduction,
and considerable savings in data analysis are accomplished.
Although improvements in the present system are desir
able, it is felt that it can be utilized with advantages in
the monitoring of PM patients. One application will be to
count on line paroxysmal events and their duration in
recording sessions, just like the neurologist would do.
The agreement in the clinical findings is. expected to be
high as shown in Table VI. Another possible application is


7
method, and Welch was able to show that the variance also
decreased with k and the reduction on resolution was also
present. Both methods give similar results, so generally
the Barlett method is preferred to save one step (Dumer-
muth, 1968; Matousek & Petersen, 1973; Hagne et al., 1973).
Although the variance of the estimate can be made
arbitrarily small, there is a trade-off for resolution.
Therefore, if an unknown spectrum is going to be estimated,
great care must be exercised not to miss peaks in the power
spectrum and at the same time trust the peaks displayed.
In EEG the modified periodogram as an estimator of the
power spectrum has been widely used. One of the pioneering
works was done at UCLA to investigate the EEG activity of
astronaut candidates by D. 0. Walter and coworkers (Walter,
1963; Walter, Rhodes, Brown & Adey, 1966; Walter, Kado,
Rhodes & Adey, 1967; Walter, Rhodes & Adey, 1967). Also,
Dumermuth and coworkers in Switzerland (Dumermuth, Huber,
Kleiner & Gasser, 1970; Dumermuth, 1968) use extensively
this technique. It has been applied in automated sleep
scoring (Walter et al., 1967; Caille, 1967; Rosadini et al.,
1968), age-dependent EEG changes (Hagne et al., 1973;
Matousek & Petersen, 1973), schizophrenia (Giannitrapini &
Kayton, 1974; Etevenon et al., 1976), studies of EEG in
twins (Dumermuth, 1968), studies of EEG background activity
(Walter et al., 1966; Zetterberg, 1969; Gevins et al.,
1975), brain lesions (Walter et al., 1967), and also drug
evaluation (Matejcek & Devos, 1976; Knkel et al., 1976).


267
TITL 'MAIN*
* MAIN
**-** $***** **<: *Scs(t £ 4¡ * j)l *

* PERFORM INITIALIZATION
* TESTS FOR REPETITION RATE
* AND SPIKE GCCURENCE (DELAY)
* FLAGS OUTPUT D/A I)
* PASSES CONTROL, TO PEAK AND
* SZURE
*
^REGISTERS USED
RATE
SPIKE
FILTER
*
R 1
REPETITION
*
R5,
6 BLV/P FCR
*
R7
8 BLViP FOR !
*
R 1 2 FLAGS
2240
AORG >2240
F080
MAIN
EOU
>FD80
FC 00
DELAY
EQU
>FC00
0030
i-RATE
EQU
>80
0034
LRATE
EQU
>34
0100
HHRAT
EQU
>100
0034
LLRAT
EQU
>B4
1EFO
ADC
EQU
>1 EFO
00 3C
TPLUS
EQU
>3C
0014
TMINU
EQU
>14
Q09E
FS
EQU
>9E
23 AO
PEAK
EQU
>23A 0
2620
SZUR E
EQU
>2620
FC 06
MASK
EOU
>FCoe
FD60
WP IKE
EQU
>FD6 0
0120
COUNT
EQU
>120
FC 08
PCI
EQU
>FC08
FC22
FLAG
EQU
>FC22
FFSA
INTWP
EQU
>FF 3 A
FD3E
WINPT
EQU
>FD3E
2000
INPUT
EQU
>2000
2490
SPIK E
EQU
>2490
2710
RESUL
EQU
>2710
FC24
SZTI M
EQU
>F C24
FC26
MASK 4
EQU
>FC26
FC28
MASK8
EQU
>FC28
2240
02E0
LWPI MAIN
2242
FD80
2244
0201
LI
1*RESUL
2246
2710
2248
C80 l
MOV
1,3SZT
224A
FC24
RAM AREA FOR SZ DATA


273


Fig. 39. Slow Wave Amplitude Versus Time (#12-3)
1
Art OS


65
It has been shown that scaling.uses most efficiently
the dynamic range of the wordlength for a particular struc
ture (Jackson, 1970). However, scaling is essentially a
method of controlling the internal magnification. If a
certain filter needs to be built, in a specific machine and
with particular structure, scaling just enables its imple
mentation with a good use of dynamic range. Sometimes this
methodology may lead to impractical filters, mainly when
microcomputers are used as the implementation medium (DeWar
et al., 1978). This motivated the search for structures
which would display reduced magnifications. Let us take as
an example the canonical structure shown in Fig. 4a and
also the structure called feedforward of Fig. 4b. They are
the only ones which will be compared in this work. Their
big advantage from the microcomputer implementation point
of view is the minimum (canonic) number of multipliers.
The internal magnification in node 1, G^, is the one which
will constrain the choice of the wordlength. As is also
known, the zeros may counteract the magnification effect of
the poles. In the canonical structure, as the feedback sig
nals are always taken before the zeros are implemented,
Gj is independent of the zero placement and number. On the
other hand, in the feedforward structure, one of the zero
forming paths is introduced before the feedback signals are
taken, allowing for decreased gains when the filter poles
are close to the zeros, i.e., in our application when the
filters are low frequency (zero at z=l) or close to fs/2


169
NAME: SUBJECT
last r irs c m.i.
TAPE = : START FOOT. :
condition!
good Gfair Dpoor Da wake
Cdrowsey Oasleep stuporous Dcomatose
lethargic
ABNORMAL ACTIVITY:
FOCAL GOIFFUSE '.ELL DEFINED CPOCRLY DEFINED
OCCURRENCE:
CONTINUOUS BURSTS SPORADIC CSPARSE
NONE
RECORDING QUALITY:
GOOD GPOOR^EXCESSIVE EMG/ARTIFACT
FOOTAGE OF INTEREST:
VIDEO TAPE USED? QYES GNO
TECHNICAL COMMENTS/OBSERVATIONS:
ENGINEER PRESENT:
Fig. 30continued


91
However, the usable signal level really depends on the
detection scheme used. For example, a sine wave of 30 Hz,
-46 dB below maximum signal, was recognized with a zero
crossing detector at the tape slowest speed (15/16"). It
also depends on which digital parameters the algorithm
uses. In speech processing figures on 20 dB between the
smallest signal that is going to be processed and the A/D
noise are frequently used (Gold & Rader, 1969).
The deterioration of the input signal to noise ratio
due to the filtering must also be taken into consideration.
It was shown (Principe et al., 1979) that for the case of
sleep EEG filters, implemented with the nonscaling design,
the noise factor of the implementation ranged from 0.45 to
2.14, i.e., yielding in the worst case a degradation of
1 bit. For all these reasons an 8 bit A/D converter is not
recommended to represent the EEG data. A 10 bit A/D
(dynamic range of 54 dB) is probably a good choice for EEG
applications. If the input of 12 bits obtained with the
present A/D converter is scaled to 10 bits, filters with
internal gains up to 64 could be directly implemented in a
16 bit microcomputer.
Structures which will introduce the lowest noise and
at the same time present the smallest magnification (i.e.,
for which the input-output gain is the limiting factor) are
desired. These specifications are in fact contradictory,
and the solution is generally a trade-off between increase
in wordlength and large signal to noise ratio. There is no


224
5) The variability of the repetition period tends to
decrease with longer seizures before the drug
administration and increased after.
6) After the drug there is a tendency to have smaller
seizures.
A few correlations were expected, but they did not
appear. For instance, a greater variance of the repetition
period with longer seizure duration (because more waves are
detected, and the EEG is a highly variable phenomenon); an
increase of half period of slow waves measured between val
ley and peak with the repetition period, as if the slow
waves were half cycles of sinusoids.
Analysis of the False Detections
and Proposed Improvement m the Detector
As was mentioned before, the system is sensitive to
some artifacts present in the EEG recording of unrestrained
patients. The worst artifact that concerns the detector
performance is chewing, since the pattern is very close to
the PM as Fig. 48 indicates.
At first, the period requirement on the slow wave
repetition rate was thought enough to differentiate the two
patterns, but it turns out that this is not always the
case (Figs. 48a and b). The problem does not seem solvable
with additional hardware for the following reasons. An
inclusion of a muscle detector in the detection scheme is
dangerous as in some patients the seizures are associated


I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Donald G. Childers
Professor of Electrical
Engineering
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Lder
of Neurology and
I certify that I have read this study and that in my
opinion it conforms to acceptable standards of scholarly
presentation and is fully adequate, in scope and quality,
as a dissertation for the degree/pf Doctor o.f Philosophy.
Arnold Paige/
Professor of\ Electricl
Engineering


51
that instead of one zero there are two. The numerator
becomes (Fig. lb)
I z-11 = 16 sm . (12)
The region of the unit circle where the two zeros give
smaller magnification is
,- 4 wT . 2 wT
16 sm < 4 sm
or
< arc sin wT < 60.
2 2
(13)
It can be said that the wide-band transformation will
yield smaller magnification transfer functions when the
filter passband falls in the region 0 experimentally verified (Balakrishnan, 1979). The narrow-
band transformation shall be used to design filters which
have passband between 60 used for filters 120 ters fall in the range 0 essentially excluded from the study. Of course, these
results must be taken as approximations since for each
transformation the pole Q's are slightly different.
The design procedure just described has been imple
mented in a Fortran IV program, presented in Appendix I.
The inputs are the frequency domain specifications of
center frequency, bandwidth, ripple in-band and out-of-
band attenuation rates. The program chooses the filter


4
To find the periodogram, the FFT of the finite EEG sequence
is taken. The finite time series can be thought of as the
multiplication of the infinite time series X(t) with a
rectangular window function of duration T. In the fre
quency domain this corresponds to the convolution of the
spectrum of X(t) with a sinf/f which introduces finite
resolution and leakage in the spectrum of X(t) and there
fore affects any spectral quantity extracted from it. The
finite resolution and leakage are always coupled together
and derive from general relations between the time (dura
tion) and frequency (bandwidth) domain transformations
(Thomas, 1969). It is only possible to improve one at
expense of: the other. One family of approximation func
tions that yield the optimum compromise (prolate spheroidal
functions) are quite difficult to implement and are seldom
used (Temes et al., 1973), so more readily available func
tions are preferred. The best solution is to deal with
each problem separately: use a window (Hammings, Kaiser,
Tukey, Barlett, see Childers & Durling, 1975) to smooth the
data which will improve side lobe rejection; and increase
the record length to improve the resolution. The last
requirement can only be accomplished at the expense of
longer computation times and is directly constrained by the
stationarity of the data. This concept deserves a further
explanation because sometimes the increase of the record
length, by appending zeros at the end of the data record,
is thought to increase the "resolution." As a matter of


CHAN 2 Digital Spike Filter
CHAN 3 Digital Slow Wave Filter
CHAN 4 Input EEG (Seizure Patient #12)
Fig. 16.
Performance of Filters in Seizure
126


310


174
number of minutes of artifacts (30 continuous sec minimum)
averaged 18 minutes per tape. They were mostly composed by
eating artifact, but telemetry out-of-tune, which produces
very high amplitude high frequency spikes as well as move
ment artifacts, were common.
The paper records from the EEG sessions had been pre
viously scored by neurologists in the Veterans Administra
tion. As the tapes did not have a time code generator
recorded, and not always was the tape started in the begin
ning of the session, the synchrony was hard to find in some
records. In these cases paper records generated while
testing the microcomputer system were rescored by the
experts.
The detector was tested by playing back the tapes
obtained during the recording sessions. One EEG channel
(always one frontal) was analyzed in real time. The cali
bration sinusoid in the beginning of each tape was used to
calibrate the system. The information obtained through the
computer detection included the paper records flagged (see
Fig. 27 of Chapter III) and the statistics which were
available in the microcomputer memory at the end of the
sessions (format explained in Chapter III). The statistics
were outputted to a printer (TI Silent 700), and to get a
permanent workable copy, they were also dumped to a cas
sette. The system's evaluation was aimed at two quanti
ties: the agreement in the detection of seizures and the
agreement in its duration. Therefore, agreement tables


139
TIBUG MONITOR AND
INTERRUPT VECTORS
(ROM MEMORY)
TMS 990/101M-1
I/O BOARD
RAM MEMORY
TMS 990/201-1
ROM MEMORY
TMS 990/201-1
RAM MEMORY
TMS 990/101M-1
0000
1000
1EF0
1EFE
2000
6000
9FFF
FFB0
FFFF
Fig. 23. Memory Mapping of the Microcomputer TMS 990/101M-1
as Used.


Fig. 11a. PM Variant (Patient #3)


212


present theory to arrive at the general rule to pair the
poles and zeros and to cascade the second order sections to
obtain the "best" solution. The following rule is sug
gested to set the pairing of the poles and zeros and the
order of the cascade. From the general analysis (every
possible combination of poles and zeros and ordering) the
first thing is to check if the greatest magnification is
implementable in the choice of the microcomputer and A/D
converter. If it is, then just choose the ordering that
2
displays the lowest 0 ut. If. the. maximum increase in .
wordlength required is too big, then choose the pairing
which is accommodated by the combination and then pick up
the ordering which has the lower noise. As the general
analysis may not be available, it is thought important to
extend the discussion (although heuristically) of the pair
ing of the poles and zeros and section ordering. For the
case of fourth order filters the rules are simple: If the
higher Q pole is realized first, then the output signal to
noise ratio can be expected higher. To realize the highest
possible signal to noise ratio, the higher Q pole shall be
paired with the zero further away from its resonant fre
quency. However, this methodology can lead to very large
magnifications (or the possibility of overflow). To obtain
a compromise between the magnification and the signal to
noise ratio, the higher Q pole shall be paired with the
zero closer to its resonant frequency and realized first.
There is no advantage in realizing the higher Q pole last,


58
Therefore, the following analysis will be restricted to
two's complement truncation and rounding. For rounding the
error is bounded by (Oppenheim Shafer, 1975)
-2b while for truncation it is
-2~b+1 x>0
0te<2"b+1
x<0
(20)
where b+1 is the number of bits of the wordlength. The
truncation error is bigger than the roundoff error, but
filters realized with truncation need fewer operations, as
truncation is readily done in the microcomputer.
Filter Internal Magnification
Fixed point arithmetic must be chosen for the imple
mentation of digital filters in today's microcomputers due
to computation time constraints. Therefore, one of the
serious problems in the implementation phase is the possi
bility of overflow in the additions. Overflow causes gross
errors in the filtered output and even the possibility of
sustained oscillations (Ebert etal., 1969).
An important consideration in the design is to ensure
that when an overflow, produced by the input, occurs, the
filter will recover in a short time. When the recovery is
short, overflow propagation is limited and the filter is


55
computing the filter recursion relation. As was said in
the introduction for EEG applications, fourth order analog
bandpass filters were found satisfactory. Following the
basic rules explained in the previous section the transfer
function for the class of EEG filters can be written as
H(z)
(z-l)p(z+l)q
(z2-C1z+D1)(z2-C2z+D2)
(17)
where
l There are three basic ways to implement (17). One is
called the direct realization and implements the fourth
order polynomial directly. The high sensitivity of this
realization to the finite length effects of the implementa
tion is well known (Gold & Rader, 1969). The other two are
the cascade and the parallel form. For filters with the
zeros on the unit circle, the cascade form can be imple
mented with fewer multipliers (Childers & Durling, 1975).
Therefore, it will be the only one studied. The variables
which condition the implementation are the type of arithme
tic (fixed or floating point), the number representation
(sign magnitude, two's complement and one's complement),
and the quantization methods (truncation or rounding).
For fixed point arithmetic, the implementation is
based on the assumption that the location of the binary
point is fixed, so numbers must be aligned before


82
Using the property of the noise autocovariance function
expressed by (34)
2
where ais given by (33). Using Parseval's relation (44)
becomes
00
cr2 = cr2 7 h2 (m) = c2-^i- H(z) H(z-^) z^dz (46)
Y em=0 e 2iqtc
where c is taken as the unit circle.
This expression is often easier to compute than the
infinite summation and will be extensively used.
The transfer function for the signal and A/D conver
sion noise are the same. Since bandpass filters will be
implemented, and the frequency spectrum of the input noise
is white, the bandwidth of the output noise is narrower at
2 2
the output, yielding effectively CTout A/D conversion noise is not the only source of noise intro
duced in the computations. As the goal is to determine the
signal to noise ratio at the output, the total noise at the
output must be evaluated including the contribution of the
A/D noise.
The result of (46) implies that the system transfer
function is realized without any error. In practice this
is not the case, but assuming the A/D conversion noise
uncorrelated with the other noise sources, the total output
noise can be evaluated by simple addition.


137
P=2592 2500
?B 2582
BP FF8fl 2582
?M FG08
FG 02=01-41!
FG 04=01-28
7-R
W=FF8R
P=2582 2500
?B 2582
BP FF8R 2582
?W FG02
FG02=014E
FG 04=01-28
?R
l.l=FF8ft
P=2582 2500
?B 2582
BP FF8P 2582
?t1 FG 02
FG02=014B
FG04=0129
7R
l.l=FF0H
P=2582 2500
7--A
ERROR 4
?B 2582
BP- FF8R 2582
?M FG02
FG 02=00132
FG04=OOBR
?R
W=FF9R
P=2582 2500
?B 2582
BP FF8R 2582
?M FG02
FC02=00D2
FG04=00Bft
?R
l.i=FF8fi
P=2582 2500
?B 2582
BP FF9R 2582
?M FG 02
FG02=00B8
FG04=00BR
D202
BE 02
BE 02
C202
G202
0202
Fig. 21
Output of CALIB Program
Different Amplitudes.
Input Sine of Two


322


204
was observed for the amplitude measures, as Figs. 36, 37,
38, and 39 show for patient #12. The other patients'
seizures had similar characteristics.
The second group of parameters was studied with sei
zure duration as the X axis. Patients #4, #5, and #7
displayed smaller repetition periods for longer seizures in
the first two sessions, but failed to show it in the third
session (Figs. 40a, b, and c) Patient #12 did not show any
trend. Patient #7, in session 1, showed a clear division
in seizure duration, i.e., long seizures and small seizure.
None of the others displayed similar characteristics.
All the patients except #4 showed a decrease in the
longest seizure after the drug administration.
The variability of the repetition period in patient #5
decreased towards longer seizures in the first two sessions
and increased in the third (Figs. 41a, b, and c). In #7
the same trend was noticed. In #12 it remained constant.
The half period of the waves remained constant across
seizure duration for patients #5, 7 and 12 (Figs. 42a and
b). The amplitude of the slow wave remained approximately
constant across seizure duration for patients #5, 7 and 12
in all sessions. In #7-3 an increase of amplitude with
duration was noticed (Fig. 43). The spike amplitude was
constant across seizure duration for all the patients.
The next set of parameters used the repetition period
as the X axis. The variability of the repetition rate
increased with longer repetition periods in #7, #5, and


Fig. 14b. Spike Filter Comparison
120


245
from the S domain frequency specifications is shown next.
The input parameters and associated format are respectively
1) Center frequency (F4.1)
2) Upper corner frequency (F4.1)
3) Sampling frequency (F4.1)
4) Ripple inband (%) (F5.2)
5) Attenuation (dB/octave) (F5.2)
6) Design type wide 1 (II)
narrow 0
A sample input is given in Fig. I-.2. The line of zeros
(actually fs=0) stops the execution. The bandpass fre
quency response in s (rad) and z (2irf/T) serve as a quick
check on the design.


190
parameter (e.g., repetition period, mean and variance
within seizure) across the session. Subsequently, the
inter and intra seizure parameters can be compared. The
estimate of the standard deviation in seizure is calculated
by averaging the variances of the parameter for each sei
zure and taking the square root; i.e.,
2
where a. refers to the variance of individual seizures
i
The estimate of the variance for the session is calcu
lated by
where is the mean for each seizure of one session and M
the number of seizures for that session.
Table VII presents these data for the six patients
analyzed. The most striking feature about the data is the
constancy of the period measurements for each subject
within sessions and from session to session.
For patients #7 and #12 the standard deviation inter
seizure is only slightly larger than the intra seizure
measure (e.g., a=0.08 intra, a=0.12 inter). Patient #5
displayed the highest standard deviation (cr=0.26). For the
group of PM variant patients the variability was much
higher for the inter seizure measures (highest cr=0.76) .
Nevertheless, the standard deviation for the intra seizure
repetition periods are comparable to the classical PM


335
Carrie, J. R. G. "A Hybrid Computer Technique for Detect
ing and Quantifying Spike and Wave EEG 'Patterns."
Electroenceph. Clin. Neurophysiol., 33:339-341, 1972b.
Carrie, J. R. G., and J. D. Frost. "Clinical Evaluation of
a Method for Quantification of Generalized Spike and
Wave by Computer." Computers and Biomed. Research,
10:449-457, 1977.
Chang, T. L. "A Low Roundoff Noise Digital Filter Struc
ture." Proceedings Int. Sympo. Circuits and Systems,
New York, pp. J.004-1008, 1978.
Chick, L., Sokol, R. J., and M. G. Rosen. "Computer-
Interpreted letal EEG: Sharp Wave Detection and Clas
sification of Infants." Electroenceph. Clin. Neuro-
physiol., 42:745-753, 1977.
Childers, D. G., and A. Durling. Digital Filtering and
Signal Processing. West Publishing Co., New York,
1975.
Childers, D. G., and A. Durling. Digital Filtering and
Signal Proceedings. West Publishing Co., St. Paul,
1975.
Claasen, T. A. C. M., Mecklenbraiker, W. F. G., and J. B. H.
Peek. "Effects of Quantization and Overflow in Recur
sive Digital Filters." IEEE Trans. Acoust. Speech and
Signal Proces., ASSP-24:517-519, 1976.
Cohen, B. A., and A. Sanees. "Stationarity of the Human
Electroencephalogram." Med. & Biol. Eng. & Computers,
15:513-518, 1977.
Cooley, J. W., and J. S: Tukey. "An Algorithm for the
Machine Calculation of Complex Fourier Series." Math
ematics of Computation, 19:297-301, 1965.
De Mori, R., Rivoira, S., and A. Serra. "A Special Purpose
Computer for Digital Signal Processing." IEEE Trans.
Computers, C-24:1202-1211, 1975.
Dewar, W. J., Chiu, L. Y., and R. Radzyner. "Microproces
sor Implementation of Digital Filters." Conference on
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Dumermuth, G. "Variance Spectra of the EEG in Twins." In
Clinical Electroencephalography of Children. Almquist
& Wiksell, Stockholm, pp. 119-154, 1968.


151
the previous slow wave threshold is restored; the pointer
to memory is saved; and control is passed to MAIN.
STATIS. This program has two parts. The first
reduces to computing the running averages of the parameters,
their square value, and counting the number of entries.
The additions are done in double precisions. The second
part is related to evaluate the mean and variance using
the relation
x =
ilx.
N 1
a =
x
Ilx2-X2,
N l
This part of the program is very sensitive to errors due to
the need for division in fixed point arithmetic. There
fore, it was decided to format the data such that most of
the bits of the registers would be always utilized.
The waveform parameters are always restricted to at
most 12 bits for the amplitude, less for the others.
Therefore, the word that stores the mean value can also be
used to output a code in the most significant 4 bits,
according to the rule;
4 data is shifted left 4
8 data is shifted left 8
C variance is shifted right 4.
To decide about the amount of shifting left possible, the
2 .
location which stores the largest quantity, Ix^, is checked
(MASK 4, MASK 8). Only the shifting of one or two digits


75
When the signals are properly scaled to avoid clipping,
(36) can be written as (Oppenheim & Shafer, 1975)
SNR = 6b-l.24 dB 6b (37)
which shows clearly the interrelationship between dynamic
range and quantization error in any signal processing
algorithm. For each bit added to the wordlength, the sig
nal to noise ratio improves approximately 6 dB.
It was stated earlier that the class of constant
inputs needs a special modelling. One case that deserves
studying is the zero input condition, since it may arise
often in real applications. Theoretically, if x(n) is zero
in (16), y(n) will then converge to zero if the filter is
assumed stable. It has been observed, however, that in the
actual system the output does not always display the theo
retical behavior. All components of the filter can only
attain a finite number of values since they are quantized.
This makes the real filter a finite state machine. An im
mediate consequence of this is that if the filter output
does not converge to zero with zero input, it must become
periodic after some finite time. The periodic oscillation
is referred to as limit cycle or zero input limit cycle
(Rabiner, 1972) and is the prototype of correlation between
noise samples. The assumptions underlying Fig. 6 are then
not applicable, and the best method for investigating zero-
input stability is the second method of Lyapunov (Liu,
1971). The general analysis is very difficult to carry
out, and here only the results will be presented for the


150
SZUKE. The first thing done in this module is to
clear the statistics workspaces, since values from previous
seizure or esporadic detections will still be there. The
other action taken is to divide by 3/4 the value of slow
wave threshold, since slow waves during seizure may decrease
in amplitude. The value of the clock, which counts seconds
relative to the program start, is also stored in memory.
The first part of SZURE is totally identical to the func
tional part of MAIN; i.e., control is passed to PEAK, and
the repetition rate is checked. As long as the slow waves
appear with a repetition rate of 28 to AO the program
just passes to statistics the value of Rl. When a desyn7
chronization occurs, the program makes sure that the last
slow wave was detected less than 1 sec ago (Rl); otherwise,
the end of seizure is recognized. If the condition is met,
control is passed to PEAK to check if the next slow wave
appears within the prescribed period (34__ to 80) If the
period requirement is met, control is passed to the begin
ning of SZURE again. If not, seizure count is stopped.
The last period that does not meet the requirements is not
counted either for the duration or for the statistics. The
seizure duration is loaded in memory; the respective sei
zure count is incremented; and control is sequentially
passed to the various STATIS programs in order to obtain
the mean value and variance of the detection parameters.
At the end, a separation tagFFFFis loaded in memory;


36
filter's frequency (or time) specifications. In the second
phase the objective is to choose filter implementations
which optimize, in some sense, the finite wordlength
effects of any practical processor. The most important
problems of the finite length effects are the finite
dynamic range of the computation, which may cause over
flows, and the finite precision of the constants, arith
metic, and input data, which produces error that may
degrade the signal to noise ratio.
It turns out that the two design phases are not com
pletely independent,as will be shown. The microcomputer
implementation is expected to be very sensitive to the
above-mentioned parameters since the arithmetic must be
fixed point (small dynamic range which increases the proba
bility of overflow) and the wordlength is relatively small,
giving a heavier weight to the finite effect errors (also
called roundoff, errors). For this reason it was thought
convenient not to separate the two design phases in order
to have a better perspective of the interactions between a
specific recursion relation and its implementation.
As various routes may be taken for digital filter
design, a criterion to compare different design procedures
(hence different implementations) is necessary. Here
design procedure means selection of appropriate transforma
tion methods to arrive at the algorithm for the filter
transfer function, with maximum simplicity in terms of


290


83
Roundoff noise in the multiplications. It is general
practice to quantize the output of the multipliers to keep
the same wordlength throughout the filter calculations.
Essentially the multiplication roundoff noise is the same
process as the A/D noise. However, the placement of the
noise sources depends upon the structure used and how the
arithmetic is actually performed. This means that, in
general, the transfer function for the multiplication
roundoff noise does not coincide with the systems transfer
function. Fig's 5a and 5c show the placement of the noise
sources (e^, &2t e^) for the feedforward and canonical
structure. If the addition was performed in double preci
sion, there would be only one noise source at the output of
the adders, but the computation time would have been
increased. Truncation of the result is accomplished by
just dropping the 16 least significant bits of the product.
To compute equation (46) the transfer function from
the noise sources to the output must be determined, along
2
with the weight of the noise sources. When the compu
tation wordlength is the same as the input number of bits,
there is no question what the weight shall be. However, in
this case the computation wordlength is bigger than the
input number of bits; hence an analysis was undertaken to
see which is the limiting factor. Actually this was a very
misleading point in the noise analysis, and so two explana
tions based in different arguments will be presented: From
the point of view of the fixed point arithmetic, before an


ho to fv) i\) ro ro ro fo
295
2000
FCE2
FDOO
F020
FD3E
l EFE
FD66
FD 84
1 EFO
7FFF
E739
0334
D1F9
D334
E355
DE 52
CAA3
DE52
2000 02E0
2002 FDOO
2004 0201
2006 D1F9
2008 0202
00A D1F9
OOC 04C3
COE 04C4
010 04C7
012 04C8
Cl4 04CC
016 0206
018 1EF0
TITL FILTER*
*
* 2ND ORDER CHESYSHEV DIGITAL FILTER PROGRAM
*
4 CHARACCTER ISTIC S SPIKE
* BANDPASS 10 TO 25 HZ
4 RIPPLE 15 %
4 ATTENUATION 12 DB/OCT
4 SAMPLING FREO 240 HZ
4
4 CHARACTERISTICS SLOW WAVE
4 BANDPASS 0*8 TO 6 HZ
4 SAME SPEC
4 SAMPLING FREQ 80 HZ
4
4 INITIALIZATION
4
AORG >2000
FIRST
EQU
>FCE2
SECND
EQU
>FDOO
THIRD
EQU >FD2 0
FORTH
EQU >FD3E
INPUT
EQU
> IEFE
GUT 1
EQU
>FD66
0UT2
EQU
>FD8A
ADC
EQU
> 1EF0
MASK
EQU
>7FFF
Cl
EQU
>E7 39
01
EQU
i >0334
C2
EQU
1 >D1F9
D2
EQU
1 >0334
C3
EQU
>E355
D3
EQU
> DE52
C4
EQU
>CA A3
C4
EQU
>DE52
4
LWPI
SECND
LI
1 C2
LI
2 C2
CLR
3
CLR
4
CLR
7
CLR
8
CLR
12
LI
6, AOC
OUTPUT OF A/D
FILTER CQEF IN HEX
DEFINE 2ND WORKSPACE
R1 GETS C2
R2 GETS D2
4


TABLE V
COMPUTER/HUMAN FINAL AGREEMENT
Human
Computer
1 < Sz < 3 sec
3 < Sz <10 sec
Sz > 10 sec
Agreement in
Seizure Detection
(# of Sz)
844
475
221
195
93
93
Agreement in
Seizure Duration
(# of Sz)
439
162
80
Total Time in
Agreement (sec)
1122
1057
1640
1420
Computer Counts
632
225
86
Computer Misses
369
26
0
Computer False
Detects
168
12
0
185


160
facilities available. Testing of a program that runs with
interrupts using a simple monitor is to be avoided, simply
because the monitor commands (e.g., breakpoint) use lower
priority interrupts, and so control is not passed to the
monitor when the breakpoint is encountered. Modifications
in instructions prior to the inclusion of the breakpoint
are a must. Besides this problem, the other facilities
available were reduced to the display of PC, WSP and status
flags, and a command that displayed the contents of the
present workspace registers.
The only attitude used to surpass this was persistence
(trial and error) and to trust the rewarding modularity of
the program. Almost all the blocks could be tested inde
pendently, which narrowed the problems enormously. The
sequence of the testing was as follows:
1) test of the FILTER program with no interrupt
2) test of the FILTER program with interrupt
3) test of the PEAK with FILTER
4) test of the PEAK with SPIKE with FILTER
5) test of MAIN with PEAK, SPIKE and FILTER
6) test of SZURE with PEAK, SPIKE and FILTER
7) test of entire system
8) test of STATIS with controlled data
9) test of STATIS with entire system.
It is worth mentioning that the availability of the two D/A
channels was of paramount importance, not only in the func
tional testing, but also in the selection of the detection


CHAN 4 Slow Wave Narrow 1 sec
Fig. 14a. Slow Wave Filter Comparison
119


171
of seizures the detector's performance was extremely good,
but the aim was to test the detector in a completely dif
ferent environment. A second group of patients was then
selected:
#3 PM variant
#4 PM variant
#5 classical
#7 classical
#12 classical
#16 PM variant.
Examples of the patterns for patients #4, #5, and #16 are
given in Figs. 116, 31, and lie, respectively. It was also
important to test the detector with data which would
reflect the unconstrained conditions of a home environment.
It was fortunate that the recordings were performed via a
telemetry link, since the patients were allowed to move and
perform everyday functions like eating, walking, etc. The
testing in "selected epochs" and in these more general con
ditions has little in common.
Three recordings, two before and one after the drug
administration, were utilized for the testing. They com
prise tapes #4, 5, 6, 7, 8, 9, 15, 17, 18, 20, 21, 24, 25,
30, 32, 39, 40, 45, 46, 53, 54, 56, 57, 72 with a total of
70 hours of data analysis, i.e., an average of four hours
per record. The number of seizures greater than 3 sec
found in each record varied from 1 (second recording,
patient #12) to 65 (second recording, patient #3). The


26
After obtaining the spectrum, some type of pattern
recognition must be utilized to judge about the presence of
certain frequency components coupled with the event, which
incidentally must assume a complete knowledge about the
background spectrum and the relations time patterns-
frequency patterns. The question arises, why not work with
the time patterns to begin with?
Another problem is how can the information from fre
quency analysis be translated to the clinician who sees
time patterns and wants information such as time of occur
rence (1 sec), duration, amplitude, etc.?
It seems a much more natural choice to use time domain
techniques.
The other technique reviewed is matched filtering,
which is the optimum detector to extract patterns from a
noisy background, when the noise is stationary and the pat
terns known. The problem with its application to EEG is
the variability of the patterns (around 10 percent,
Smith, 1978) and the drastic change in the power of the
noise (background activity), which deteriorates the detec
tor performance. Yeo (1975) was able to show that a zero
crossing detector, although not optimum, performed better
when the patterns were allowed to vary. The false alarm
rate of the detector is also independent of the noise
power.
The technique which detects nonstationarities in the
EEG have some drawbacks besides being computationally


341
O'Donnell, B., Berkhout, J., and W. R. Adey. "Contamina
tion of Scalp EEG Spectrum during Contraction of
Cranio-Facial Muscles." Electroenceph. Clin. Neuro-
physiol^, 37:145-151, 1974.
Oppenheim, A. V., and R. W. Shafer. Digital Signal Proc
essing. Prentice-Hall, Inc., New Jersey, 1975.
Oppenheim, A. "Realization of Digital Filters Using Block
Floating Point Arithmetic." IEEE Trans, on Audio and
Electroacoust., AU-18:130-136, 1970.
Parker, S. R., and S. F. Hess. "Limit Cycle Oscillations
in Digital Filters." IEEE Trans. Circuit Theory,
CT-18-.687-697, 1971.
Peled, A., and B. Liu. "A New Hardware Realization of
Digital Filters." IEEE Trans, of Acoust. Speech and
Signal Proces., ASSP-20:456-458, 1974.
Peled, A. Digital Signal Processing. John Wiley & Sons,
New York, 1976.
Persson, J. "Comments on Estimation and Tests of EEG
Amplitude Distribution." Electroenceph. Clin. Neuro-
physiol^, 37:309-313, 1974.
Pfurtscheller, G., and G. Haring. "The Use of an EEG Auto
regressive Model for the Calculation of Spectra Power
Density." Electroenceph. Clin. Neurophysiol., 33:113-
115, 1972.
Pola, P., and 0. Romagnoli. "Automatic Analysis of Inter-
ictal Epileptic Activity Related to Its Morphological
Aspects." Electroenceph. Clin. Neurophysiol., 46:227-
231, 1979.
Principe, J. C., Smith, J. R., and A. Paige. "Microcom
puter Based Digital Filter for Electroencephalogram
Processing." Proceedings IEEE Southeastern Confer
ence, Atlanta, pp. 24-28, 1978.
Principe, J. C., Smith, J. R., Balakrishnan, S. K., and
A. Paige. "Microcomputer Based Digital Filters for
EEG Processing," IEEE Trans, of Acoust. Speech and
Signal Proces., in Press.
Pusey, L. C. "High Resolution Spectral Estimates." Tech.
Note, 1975-77, Lincoln Lab, MIT, 1975.
Rabiner, L. R. "Terminology in Digital Signal Processing."
IEEE Trans. Audio Electroacoust., AU-20:322-337, 1972.


companionship in spite of the stress created by the long
working hours devoted to the laboratory.
iii


247
501
503
502
1
500
101
too
DESIGN OF CEaV3HFV DIGITAL FILTER
MUST *E SUPOLTEO CENTER FFEOUSNCY WO,CUTtjFF FREQUENCY wC.RlRPLg
PERCENTAGE In PA3SbA.NO PR AIQ OSSIficQ ATTENUATION IN OS/GCTAVE AQE
C
c
12
It
3
c
13
0
c
50
|2
3Q
23'
5
14
6
C
A NO PER IQO OP -3 A NR
COMPLEX HC.WCj.TC.
,tnr T
_ 5SC50).PZt5O},wCBH,ACP,PSl(t0O),PS2(5C).2T,7KA(100J
200 3 .QN. *H,.mag (1001 ..A.WCC Cl 00) TCl.P3Z.WcTn 00)
DIMENSION TY 100) ,WP(100).PRE15C),PTMCSOi.TPbf1003, WC3C)00).TXPC100)
10),AMAG!(EC),MAC2f50),(too).AMAGflOO).PHASEC100),AMA02f100)
DIMENSION X (51 £1 v (51?) ,fiN(3) .INV (64) ,3(4,4) ,AIHPC256 3 .AX(25fc) .
!AFREfl(256)
SC Tg 502 .
hRIT£(6,503)
FORMAT C!ho,48H EXrEEDFD SPECIFICATIONS FQR A 2N0 ORDER FILTER )
CONTINUE
DO 1 lal.PO
PS(!3CMPLXfC.Q.0.Q)
PZCI)CMPLX(.0,0.0)
PT ARCOS C-1.)
READ(5,100) F0.FC.F5.PR.AQfi,HID,MHISh
TF (FS.Eo.a) STOP
wITE(h,iflil FO.Fr.FS.PR.AOP
F0RNAT(3FA.\,2FA.g]
F0PMAT(3Fa.i,cF5.2,2Il)
W02 *PT *F0-
WCU2*PI*rC
WbawCU-wO
Tat/FS
CALCULATtON-QF BP.4lL.CM
fcaSPRTCl ,/(t .-P)**P-i .)
calculation cie roer op polynomial
uNaALOG(2.*SQRTflo,**(AOfl/lO.)3/£3/(ALQG(2.*SfiRr(3.)))
n*ON
NaM+l
OH 12 la 1,20
2ITE (6,11)
ForpaT(IHC)
WRITE 16,2)N
F0HMAT(!HO.5QX,?iuDR0Eft OF POLYNOMIAL a,i2)
IFCN.5T.2) 00 TO ¡01
CALCuLATION.aF rHP POLES *03 THE LOW Pa.S3 FILTER
RsSORT(1-/E**2+!
HSFl2=0.5n*(R**(r,/Nj-5**f-1./N)3
MCFT2aO,50*fR**(t'/Nj*R**f-l,/N))
CO 3 1*1,M .
A T aFi 0* T ( 7 ) -1
PRE(I}a-HSFT2*STNf(2.*AT+l.)*PI/(2.*NJ)
PTH(I)aHCTIP*COS(f2.* A I + 1,J*PI/(2,*N))
PS(I)CMPLX(PPE(I).PIH(I))
WRITE6,13)
F0NMaT(1*M ,40X,t6HP0LES I S PLANE)
WRITE(6,40)(PS(T).Jal.M
FORHatiho,40*,3Hp5,?Fi2.7)
CONTINUOUS LOw A3S Filt£R
TCQaO.Q
00 30 M1 IOC
TCCHPLX(1.0,0.0)
WH(M)FLOATC.M-n *0,02
nCHaCMPLX fC.O.HH(w))
DO 20 Ji,H ,
TC*TC*(WC-PS(U))
TW A(M)*TC -
STaCAaSl,/TC)
IF(STW-TC0)30.3O,2s
TCQagTK
CCNTJMUE
On 3T .Mat,100
TK?M)*CASa./(TrO*TVA(M))l
DO 5 Tal, to
WRXTE(6,14)
FOHHATcIho)
ORITE(6,61
FORMAT(sqx,23HPLQT OF LOw PASS RILTCS)
CAUL PLOTrWH.TK,100)
POUFS IN Z plane
IF (nHIGH.EO.I) GO TO 140
PSZCuP!..X(O.0!O)
if (nniD.Eq.I) sc TO 131
NNaN/2


340
Lopes da Silva, F. H., Dijk, A., and M. Smits. "Detection
of Nonstationarities in EEG Using an Autoregressive
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Stuttgart, 1975.
Ma, K. M., Celesia, G. G., and W. P. Birkemeier. "Non
linear Boundaries for Differentiation between Epilep
tic Transients and Background Activity." IEEE Trans.
Biomed. Engng., BME-26:288-290, 1977.
Matejcek, M., and J. E. Devos. "Selected Methods of Quan
titative EEG Analysis and Their Application in Psycho
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Matejcek, M., and G. K. Schenk. "The Iteractive Interval
Analysis." Electroenceph. Clin. Neurophysiol., 37:104,
1974.
Mathieu, M. "Analyse de l'EEG par Prediction Lineaire."
Rapport Interne, Lab. Theory des Systems, Paris, 1970.
Mathieu, M. "Analyse de l'electro-encephalogramme par Pre
diction Lineaire." These de Docteur-Ingenieur, Paris,
1976.
Matousek, M. "Frequency Analysis; Processing of Data."
Handbook of EEG Clinical Neurophysiol., 5A:61-66,
1973.
Matousek, M., and I. Petersen. "Frequency Analysis of EEG
in Normal Children and Adolescent." In Automation in
Clinical Electroencephalography. Raven Press, New
York, pp. 75-102, 1973.
McEwen, J. A., and G. B. Andersen. "Modeling of Station-
arity and Gaussianity of Spontaneous EEG Activity."
IEEE Trans. Biomed. Engng., BME-22:361-368, 1975.
Meron, P., Sekey, A. A., and E. Zeheb. "Design Methods for
Stable Digital Filters." IEEE Trans. Acoust. Speech
and Signal Froces., ASSP-22:196-203, 1974.
Mick, J. R. "Digital Filter Design." EDN, pp. 24-26,
December 1975.
Mullis, C. T., and A. Roberts. "Synthesis of Minimum
Roundoff Noise Fixed Point Digital Filters." IEEE
Trans. Circuits Systems, CAS-23:531-562, 1976.


TABLE IVcontinued
PATIENT #16
Human
Computer
1 < Sz < 3 sec
3 < Sz <
10 sec
Sz > 10
sec
Agreement in
Seizure Detectior
(# of Sz)
51
31
18
19
5 ^
5
Agreement in
Seizure Duration
(# of Sz)
28
13
4
Total Time in
Agreement (sec)
78.4 ^
97.9
57.4
64.6
Computer Counts
43
15
4
Computer Misses
20
1
0
Computer False
Detects
8
0
0
181


8
Sometimes the power spectrum is not the only parameter
used. Dumermuth et al. (1972) uses the bispectrum, that
is, the Fourier transform of the second order autocorrela
tion function R(t]_, t2, to investigate coupling
between EEG frequencies. Incidentally, the bispectrum
analysis shows that, unless for the a and 3 frequency
bands, the function is practically zero, as would be the
case for a Gaussian random process. The coherence spectrum
ratio of the square of the cross spectrum over the spec
tra of the individual waveformsis also used to investi
gate correlation between two EEG channels (Dumermuth et
al., 1972; Walter et al., 1967).
The most bothersome question in the application of the
periodogram as an estimator is the fact that there are no
"best criteria" to determine the combination, window
duration-overlap for a particular data sequence. That is
one of the reasons why other more consistent methods (in
the sense that an error criterion can be defined and leads
to a minimization), as the autoregressive (AR) and auto
regressive moving average (ARMA), have been recently intro
duced (Fenwick et al., 1967; Isaksson, 1975; Gersch &
Sharp, 1973). The assumption behind their application is
that the EEG sequence selected is a sample from a station
ary time series. Therefore, it can be modeled as the out
put of a linear system (if transients are excluded) with a
white noise input. The output can then be interpreted as
the linear superposition of the natural modes of the system.


sec
LO
CN
AWAKE
SLEEP

1 hour
Fig. 35. Sz Duration Versus Time (#4-2)
203


Page
APPENDIX
I CHEBYSHEV FILTER DESIGN 239
Chebyshev Polynomials 239
Automated Design 242
Filter Design Program . . 244
II DIGITAL FILTER IMPLEMENTATION 250
Preliminary Considerations 250
Implementation of the Filter Algorithm . 253
III FLOW CHARTS AND PROGRAM LISTINGS 265
REFERENCES 333
BIOGRAPHICAL SKETCH 346
v


311
5


107
false positive rate. The performance of the detector will
be closely studied to individualize the activity which
produced the false detection, and software methods of
second scoring will be attempted to improve the detector's
performance.
In summary, the model for the PM activity which will
be implemented in the microcomputer is as follows:
1. Define the beginning of the seizure by three slow
waves with a three 3 Hz repetition rate as well as the
presence of at least 1 spike in the same time period.
2. Within the paroxysm require only the existence of
slow waves with the 3 Hz repetition rate.
3. Allow for desynchronizations (up to 1 sec) in the
middle of the seizure and decrease the amplitude threshold
3/4 for slow wave detection.
The individual seizure elements will be modelled as
the following:
Spiketriangular wave with a sufficient amplitude and
period requirements.
Slow wavesinewave of sufficient amplitude and with a
prescribed peak to valley duration.
Definition of the Implementation Scheme
The goal is to implement a detector which will analyze
one channel of EEG in real time, employing a microcomputer.
The choice of a microcomputer reflects the compromise of
power and versatility versus compactness and availability.


162
detected, the control was returned to the monitor. The
value on the counter was 151H. The execution of the incre
ment plus jump instruction is 20 clock cycles; therefore,
the time left (with a 3MHz clock) is 2.24 ms. This really
means that by keeping the same sampling frequency and
making small modifications in the program flow (divide the
statistics generation through two samples after seizure),
two channel processing is feasible in real time.
The other important test was consistency in the detec
tion. For sake of individualizing the problems, it was
investigated at two levels: the level of seizure detection
and the level of waveform detection and characterization.
The system consistently detected the same seizure. How
ever, it did not always detect the same waveforms. The
discrepancies were borderline cases, but nevertheless they
affected the statistics and even (but seldom) the seizure
duration. Table III shows a typical example.
The sources of the problem were reduced to three: one
analog, speed drift or tape drop outs and two digital
asynchronous sampling and roundoff noise. The last one was
eliminated by shifting right the output of the filters such
that the least significant bit was noise free (which is
possible through the noise calculations). The second dig
ital source can potentially cause problems, since the pre
cision on the periods is 10 percent and the precision on
the amplitude measures vary between 1 percent (slow wave)


129
0.53 sec (80)
n
and
0.22 sec (34h)
to detect the beginning of all the seizures analyzed, which
corresponds to frequencies of 4.5 to 1.8 Hz.
One important aspect of the period windows shown is
its enormous width. The higher value is at least double
that of the lower corner, which really shows the high
degree of variability of the patterns from patient to
patient. Special care was taken to select the "learning
set" such that it would make the detection parameters as
universal as possible.
The use of multiple detection (e.g., the detection of
the half waves and the detection of the periodicity)
deserves further explanation. In a sinusoidal wave it is
clear that both detections would be redundant. However,
the PM activity at the output of the slow wave filter seems
periodic but not sinusoidal. It can be approximated in
most of the cases by a clipped sine (the spike appearing
in the "clipped" portion, see Fig. 14). It seems then
logical from a characterization point of view to detect
each slow wave and also the period of the slow wave with
clipped portion, since more information can be gained from
the analysis. Another advantage is related to the versa
tility of the detection scheme. If the periodicity of the


282


20
(Buckley et al., 1968; Ktonas, 1970; Walter et al., 1973;
Gevins et al., 1975). This was achieved by monitoring the
first and second derivatives of the EEG and comparing them
with a fixed threshold set for each patient. The parameter
was found generally unsatisfactory since differentiation
increases the energy of the incoming signal at high fre
quencies (i.e., extends the bandwidth) and the detection
system becomes very sensitive to muscle artifacts. The
same basic idea was further improved by Carrie (1972a,
1972b, 1972). He established a moving threshold set by
background activity. Although the system was still sensi
tive to high frequencies, since they biased the threshold,
he reported better results. Gevins et al. (1975, 1976)
also used the curvature parameter (second derivative), but
to improve the system performance the duration and fre
quency of occurrence are also introduced in the detection
criteria. The threshold is automatically set for each
patient by an empirical algorithm.
A more complex model of abnormal spikes which included
different slopes for the leading and trailing edges of the
spike, plus a parameter related to the time it takes the
wave to reach maximum slope, was introduced by Ktonas and
Smith (1974), and it seems to describe fairly well spike
activity. Smith (1974) used some of these parameters to
implement a spike detector that gave good agreement without
adjustment of detector thresholds. Basically, it consists
of a set of gated monostables with "on" times related to


188
TABLE VI
PERCENT REDUCTION IN SEIZURES,
COMPUTER VERSUS HUMAN
*No third record.


Gi
Fig. 5d. 4th Order Filter.
OICTi,
-4
H
Canonic Form (ID) with Scaling.


well known the succession of a spike and a slow wave in PM
epilepsy. However, the work of Johnson (1978) showed the
sensitivity of the detector performance to this rule.
Although spike and wave is a good indicator in the begin
ning of the paroxism, the probability of a change in pat
tern in the middle of the seizure is very high. From a
three month experience in watching neurologists scoring
EEG's it became apparent that the important visual param
eter in scoring a PM seizure is the pattern in the begin
ning of the ictal event, that is, the first spike and wave
complexes. From then on, the scorer overlooks the pattern,
and his main criterion to define the end of paroxism is the
amplitude information of the EEG tracing. However, the
intersubject amplitude variability both in the EEG and in
the PM pattern discouraged the use of an amplitude criterion
as the leading parameter. It was decided to try the repe
tition rate as an alternate leading criterion, since it is
the most striking appearance of the pattern and there is no
normal periodic activity in the EEG at this frequency. As
a result it was decided to recognize the beginning of the
PM event by a spike followed by three slow waves with a
3 Hz repetition rate. A word must be said about this
choice since it could be made much more restrictive, for
instance, a spike/slow wave/spike/slow wave/spike/slow
wave, decreasing enormously the possibility of false detec
tions. There are some types of PM, called PM variant which
display a pattern similar to the classical PM but where the


78
where p is the period of the oscillation. A few points
about limit cycles are worth noting. Filters implemented
with rounding possess much smaller stability regions than
when implemented with truncation. Filters using floating
point arithmetic may possess large amplitude limit cycles.
In fixed point arithmetic the limit cycle amplitude is
generally small (within the noise floor of the filter).
It is a general rule that when the amplitude is high, the
source of the oscillation is caused by overflow nonlinear
ities (Claasen et al., 1976). Each implementation of the
same second order structure will display its own stability
region, the one presented being just a guideline.
As the study of zero input limit cycles is very easy
to accomplish with the real filter, further discussion will
be postponed to the implementation phase.
Coefficient quantization. Usually the coefficients of
a digital filter are obtained by a design procedure which
assumes very large precision. For practical realizations
the coefficients must be quantized to a fixed, small, num
ber of bits. As a consequence, the frequency response of
the actual filter deviates from the ideal frequency
response. Actually this effect is similar to the effect of
tolerances in the analog components.
There are two general approaches to the analysis. The
first treats coefficient quantization errors as intrinsi
cally statistical quantities, and the effects of the
quantization can be modelled as a stray transfer function


H +
y
Fig. I.I-3. Second Order Filter. State Space Representation.


164
and 10 percent (spike), using (54) and the triangle model
for the spike, respectively.
To improve the precision, the sampling frequency must
be increased, which is possible but not desirable (filter
gain, computation time). The approach followed was to
choose the limits of the parameter window in a region where
the errors would not be critical for the detector's per
formance. The explanation may seem dubious, but it can be
concluded, from the data analysis, that the probability
density function of the amplitude and period of the EEG
waves is not uniform. There are period and amplitude
extremities that gave fairly consistent results in spite of
the imprecisions at the component level. The only explana
tion is the relatively small number of waves that appear
close to the edges. The period and amplitude limits chosen
tried to reflect this fact.
From the tape recorder specifications, it seems that
the wow-and-flutter is a second order effect (.05 percent
at 1 7/8"/sec). The tape drop-outs are very difficult to
quantize, but are also considered a potential problem in
the playback of high frequency components.


43
axis. As the Q is proportional to the ratio w/cr, the higher
frequency poles always possess greater Q. For narrow-band
filters the difference is small, but it can become quite
appreciable for wide-band filters. Hence, the narrow-band
does not transform the time characteristics (overshoot,
group delay) of the lowpass design (Blinchikoff, 1976).
However, it is widely used due to its simplicity.
With the wide-band transformation, the poles of the
bandpass filter lay in a straight line from the origin,
ensuring that the ratio w/a is constant. The impulse
response of the bandpass filter is a time scaled version of
the lowpass. The disadvantage of the wide-band is a more
tedious design procedure. It will be shown later that the
different characteristics of the transformations will be
valuable for the control of the frequency response of the
digital filter and the finite length effects of the imple
mentation.
Transformations to the Z Plane
Now that the bandpass pole locations are known, it
will be seen how the Z plane pole pairs can be obtained.
Basically there are two different types of mapping rules
from the S to the Z plane. One, the rational transforma
tions, map the entire jw axis onto the unit circle. There
are several ways this can be accomplished (a series expan-
sion of e ), but the lowest order approximation is the
bilinear transformation given by


23
of the envelope of waveform are estimated, and the higher
order component is taken as the mean.value; the second step
is an iteration procedure and uses the result of the pre
ceding analysis. The process is repeated until a feature
less waveform is obtained. With these wave components the
half waves analysis is used to extract further information.
The appealing property of this method is the relatively
small computation involved (compared to the FFT) and the
strict resemblance with the visual (pattern) analysis.
Gotman and Gloor (1976) describe and evaluate a set of
parameters to describe the EEG at the waveform level. The
technique can therefore recognize phasic interictal events
in the EEG. Its main application is to generate informa
tion about epileptic focus and degree of abnormality of a
particular record. No mention is made on its use in the
detection and quantification of generalized seizures. The
other work reviewed fell in one of the previously described
methods. Vera and Blume (1978) use the derivative method
to analyze on line 16 channels of EEG. Chick et al. (1976)
use a scheme similar to Smith (1974).
As far as petit mal (PM) activity is concerned,
Jestico et al. (1976) use a bandpass filter 2-4 Hz to
detect the slow wave component and measure the duration of
the paroxysm. Kaiser (1976) used the duration of the spike
and of the slow wave monitored at a certain voltage level
to detect the PM activity. In a PDP-12 Ehrenberg and Penry
(1976) used zero crossing information and a measure of


CHAN 1 Input EEG
CHAN 2 Slow Wave Filter 2 sec
CHAN 3 Detections: Up S.W.
Down Spike
Fig. lid.
PM Variant (Patient #21)
106


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AUTHOR: Principe, Jose
TITLE: Automated Detection and Quantification of Petit Mai Seizures...
PUBLICATION DATE: 1979
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339
Johnson, A. A. "Automated Detection of Petit Mai Seizure
Waveform in EEG." Master's Thesis, University of
Florida, 1978.
Jones, R. H. "Identification and AR Spectral Estimation."
IEEE Trans. Automatic Control, AC-19:894-898, 1974.
Kaiser, E. "Telemetry and Video Recording on Magnetic Tape
Cassettes in Long-Term EEG." In Quantitative Studies
in Epilepsy. Raven Press, New York, pp. 279-288,
1976.
Kalman, R. E. "A New Approach to Linear Filtering and Pre
diction Problem." Trans. ASM. J. Basic Engng.,
Ser. D82, 1960.
Kawabata, N. "A Nonstationary Analysis of the Electroen
cephalogram." IEEE Trans. Biomed. Engng., BME-20:444-
452, 1973.
Ktonas, P. K. "Automatic Detection of Abnormal Spikes in
EEG." Master's Thesis, University of Florida, 1970.
Ktonas, P. K., and J. R. Smith. "Quantification of Abnor
mal EEG Spike Characteristics." Computers in Biology
and Medicine, 4:151-163, 1974.
Knkel, H.} Luba, A., and P. Niethardt. "Topographic and
Psychosomatic Aspect of Spectral EEG Analysis of Drug
Effects." In Quantitative Studies in Epilepsy. Raven
Press, New York, pp. 207-224, 1976.
Larsen, L. E. "An Analysis of the Intercorrelation among
Spectral Amplitude in the EEG: A Generator Study."
IEEE Trans. Biomed. Engng., BME-16:23-26, 1969.
Larsen, L. E., and D. O. Walter. "On Automated Methods of
Sleep Staging by EEG Spectra." Electroenceph. Clin.
Neurophysiol., 28:459-467, 1970.
Leader, H. S., Cohen, R., Weithrer, A. L., and C. A.
Caceres. "EEG with a Digital Computer." Electroen
ceph. Clin. Neurophysiol., 23:566-570, 1967.
Lee, Y. W. Statistical Communication Theory. Wiley, New
York, 1960.
Levinson, H. "The Wiener RMS Error Criteria in Filter
Design and Prediction." J. Math. Phys., 25(4):261-
278, 1974.
Liu,
B. "Effects of Finite Wordlength on the Accuracy of
Digital FiltersA Review." IEEE Trans. Circuit
Theory, CT-18:670-677, 1971.


271


63
max k
. -jX, ~2j X
ag+a^e +a2e
-jX -2j X
1+b^e +t>2
< 1
(27)
where ag, a-^, a2, b-^, b2 are the coefficients of the second
order filter. This scaling policy is sometimes too opti
mistic, that is to say, it may lead to overflow. A third
approach uses the frequency domain relation Y(z)=H(z)X(z).
00 2
The energy of the output signal is £ y, which by
k=0 K
Parsevals relation means
"2 1 ,2tt -n -ix
Joyk 5t/0 Y(e )y(e )dX-
(28)
Using Schwartz inequality
.2 ,,2ir_. ,jX., -jX
2ir
I y£ < (L H(eJA)H(e~JA)dX(-/ X(ejX)X(e"jX)dX)
k=0
2ir-'o
00 "5 2 It X
< J Xk/n H (e^ ) H (e_:l ) dX. (29)
k=0 0
Therefore, scaling constants K may be chosen satisfying
2 IT 2 -i }
/0 k H(eJA)H(e JA)dX <: 1. (30)
Again, in some applications this policy would be too opti
mistic (Gold & Rader, 1969). There is available a general
theory, which enables signal modelling by constraining the
input norms (Jackson, 1970). For the EEG analysis a


327


313
TITL TOTALS*
4444 *444444444444 4 **4**44444444444444
4 TOTALS
4444 444 444 44444 44 4 4*4 4 44 4 4 44444 444 444
4 PROGRAM to EVALUATE MEAN AND VAR.
4 OF PAIRS OF PARAMETERS OBTAINED
240 C
4
4
4
4
4
4
4
4
4
4
4
4
4
FROM THE DATA ANALYSIS.
FC00- DISPLACEMENT FROM SEPARATION
TAG TO DESIRED PARA.
FD63- ADDR. OF LAST SEPARATION TAG
+2.
PROGRAM ASSUMES DATA IN ADOR. 2720.
IT SHALL 3 E USED WITH STAT1 PROGRAM.
Rl- MEAN VALUE
R4 VARIANCE
C IN MOST SIGN DIGIT MEANS VARIANCE
IS 1 HEX DIGIT HIGHER
AORG >2400
F068
WOATA
EQU
>FD 68
FC22
FLAG
SOU
>FC22
FD80
*STA 1
EQU
>FD8Q
2580
ST ATI
EQU
>2580
FDAO
MS T A 2
EQU
> FDAO
2580
STAT2
FQU
>2580
F COO
ADOX
EQU
> F CO C
FC30
MASK1
EQU
> FC3G
FC32
MASK 2
EQU
>FC 32
2720
CRIG.N
EQU
>2720
FFFF
KEY
EQU
>FFFF
0080
MON IT
EQU
>ooao
240 0
2402
0250
FD 68
LWPI
WDATA
2404
2406.
04 EO
F C 22
CLR
2FLAG FLAG FOR TOTALS
240 8
240 A
0201
FD80
LI
1 >FD80
240C
04D1
LOOP
CLR
41 CLEAR WSP
2 40 E
05C1
INCT
1
241 0
2412
0281
FOCO
Cl
1.>FDC0
24 1 4
16F8
JNE
LOOP
2416
2413
0201
OFFF
LI.
1 > 0 FFF
241 A
24 1C
C801
FC30
MOV
1,3MASK1
24 1 E
2 420
0201
FO 00
L I
1 >F 00 0


127
Fig. 17. Two Period Measures for Slow Wave


323


94
ensured, further research shall be done in this area,
including design procedures which use more than the minimum
number of multipliers. As everything seems to be nonlinear
in this research area, a small increase in the processing
time may lead to appreciable savings on computation word-
length, for a given output signal-to-noise ratio.
!


232
Fig. 50. Performance in Movement Artifact


41
out-of-band attenuation rates. The use of Chebyshev
polynomial is suited for this goal as shown in Appendix I.
The procedure to determine the Chebyshev lowpass goes
as follows;(Principe et al., 1978):
1. From a given ripple factor (e) in the passband,
the lowpass filter poles can be obtained from (1)
2. To determine n, the polynomial order from the
attenuation in dB/OCT, (3) can be used.
sk = -sin h+2 sin(2|t),r
+ j cos hcj>2 cos (--)7T
(1)
sin hcf>2
jF"* ? tW S'
(2)
cos h4> 2
+ i +
n
n
log(2 + /3)
(3)
Lowpass to Bandpass Transformations
After designing the lowpass filter transfer function,
the bandpass can be obtained using one of the standard
transformationsthe narrow-band or the wide-band


297
*
*
SET
UP OF TMS 9901 AS A TIMER
2076
02 OC
LI
12.>100 R12 HAS ADDR OF 9901
2073
0100
207A
1 EOO
SBZ
0 ENABLE INTERRUPT
207C
1003
S80
3 PRIORITY SET TO 3
207E
0300
LIMI
3 SET INT MASK
203C
0003
2 032
0200
LI
0.-3 9901 FOR IMMEDIATE INT
2084
0003
2086
33C0
*
LDCR
0.15
2 083
10FF

JMP
$
203A
1 000
NCP
WAIT FOR INTERRUPT
2 03 C
0 2E0
LWPI
SECND
208E
FDOO
2 09 0
0205
BACK
LI
5 ..MASK
2092
7FFF
2094
49 85
SZC
5.a>C{6) END OF CONVERSION?
2096
oooc
2093
1 3F3
JEQ
BACK NO,JUMP BACK
2C9A
os ec
INC
12 SKIP TO SET 80 HZ
2 09 C
028C
Cl
12.3
2C9E
0003
2 CAO
1123
JLT
SLOW
20 A 2
C2A6
MOV
a>E(6)lO RIO,RECEIVES DATA POINT
20A4
OOOE
20A6
oaiA
SR A
10,1 SCALE INPUT
*
CALCULATION OF 1ST RESONATOR
*
THE
RECURSION RELATION IS
4
X 1 +=
-DX2+£+C(Xl+E)
4
X2 + =
Xl + E
*
y=x2
*
REGISTER USED
*
REGISTER 10 FOR INPUT E
*
REGISTER 7 FOR XI
*
REGISTER 3 FOR X2
20A3
0743
ABS
3 GET SIGN OF Y
20AA
38C2
MPT
2,3 DX2 IN R3 R4
20 AC
1 10 1
JLT
POST 1 JUMP IF P.3 PCS
20AE
0503
NEG
3 IF NEG COMPL R3
2 03 0
A OCA
POST 1
A
10,3 -DX2+E IN R3
2032
C243
MOV
3,9 SAVE IT IN R9
2084
A1CA
A
10,7 Xl+E IN R7
2056
C0C7
MOV
7,3 Xl+E IN R3
2088
0747
ABS
7
2 08 A
39C1
MPY
1 ,7
208C
1503
JGT
POST 2
2 0BE
0 A17
SLA
7,1 ALLIGN BINARY POINT
2 0C 0
0507
NEG
7
20C2
1001
JMP
POSTS


189
a certain period and amplitude are required, the computer,
after recognition, has available the exact period and
amplitude for that specific slow wave. This enables the
generation of statistics about the detection parameters,and
a much more precise description of the ongoing EEG activity
can be gained.
With the PM detector described in Chapter III it was
possible not only to present the time of occurrence and
duration of each paroxysm detected but also for the first
time to obtain the following:
1) the mean and variance of the PM recruiting period
as measured by the time between peaks of the slow
waves.
2) the mean and variance of the half period of the
slow waves as measured between the peak and the
valleys of the slow wave filter output.
3) the mean and variance of the delay between the
spike and the slow wave measured between slow wave
peak and the spike peak.
4) the mean and variance of the amplitude of the fil
tered slow wave.
5) the mean and variance of the amplitude of the fil
tered spike.
These parameters are stored in the microcomputer mem
ory using the format explained in Chapter III. At the end
of each data collection, programs TOTALS and STAT 1 can
generate the mean values and variances for each detection


336
Dumermuth, G., Huber, P. J., Kleiner, B., and T. Gasser.
"Analysis of the Interrelation between Frequency Bands
of the EEG by Means of the Bispectrum." Electroen-
ceph. Clin. Neurophysiol., 31:137-148, 1970.
Dumermuth, G., Gasser, T., and B. Lange. "Spectral Analy
sis of EEG Activity in Different Sleep Stages in Nor
mal Adults." European Neurology, 7:265-296, 1972.
Dumermuth, G., Gasser, T., and B. Lange. "Numerical Analy
sis of EEG Data." IEEE Trans. Audio Electro Acoustics,
AU-18:404-411, 1970.
Dumermuth, G., and T. Keller. "EEG Spectra Analysis by
Means of FFT." In Automation of Clinical Electroen-
cephalography. Raven Press, New York, pp. 145-160,
1973.
Durbin, J. "The Fitting of Time Series Models." Rev.
Inst. Int. Statis., 28:233-243, 1960.
Ebert, P. M., Mazo, J. E., and M. C. Taylor. "Overflow
Oscillations in Digital Filters." Bell Systems Tech.
J^, 48:2999-3020, 1969.
Eftang, P. "Automatic Detection of Spike and Wave Complex
in the EEG Using a Minicomputer." Electroenceph.
Clin. Neurophysiol., 38:209, 1975.
Ehrenberg, G., and J. Penry. "Computer Recognition of
Generalized Spike-Wave Discharges." Electroenceph.
Clin. Neurophysiol., 41:25-36, 1976.
Elul, R. "Gaussian Behavior of the EEG: Changes during
Performance of Mental Task." Science, 164:328-331,
1969.
Elul, R. "Statistical Mechanism in Generation of the EEG."
Progress in Biomedical Eng. Vol. 1. Spartan Books.
Washington, 1967.
Etevenon, P. R., Rioux, P., Pidoux, B., and G. Verdeaux.
"Fast Fourier Analysis of the EEG." In Quantitative
Analytic Studies in Epilepsy. Raven Press, New York,
pp. 355-374, 1976.
Fenwick, P. B., Mitchie, P., Dollimore, J., and G. W.
Fenton. "Application of the AR Model to EEG Analysis.
Aggressologie, 10:553-564, 1969.
Fettweis, A. A., and J. Meerkitter. "Pseudopassivity, Sen
sitivity and Stability of Wave Digital Filters," IEEE
Trans. Circuits and Systems Theory, CT-19:668-673,
1972.


Fig. 5a. 4th Order Filter. Feedforward Implementator!.


PC 14
SCALE
ECU >FC14
FC 16
LIM 1
EQU >FCl 6
FC1A
STORE
EQU >FC1A
239A
INTEN
EQU >2
39 A
2000
02EO
LWPI
PLOT
2002
FD80
2 004
02 01
LI
1 >BFF
2006
OBFF
2008
C801
MOV
1.30LDX
2 00 A
FC06
2 00C
caoi
MOV
l.aCLDY
200E
FC08
201 0
0201
LI
1> 3FFF
2012
BFFF
2014
CS01
MOV
1 ,a MASK
2016
FC 12
2013
0201
LI
1>800
2 01 A
0800
20 1C
C301
MOV
1.acONST
201 E
FC04
2020
0201
LI
1.> BPF
2022
OSFF
2024
CS01
MOV
1, as CALE
2026
FC 1 4
2028-
0201
LI
1, >140 0
2 02A
1400
202C
C301
MOV
ia l i m
202E
FC16
2 03 0
02 OA
LI
10,>FC04
2032
FCC4
2C34
02 09
LI
9 t>1EF0
2 036
1EF0
2038
0 20C
LI
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2 03A
239A
203C
02E0
LWPI
WQ AT A
203 E
FD68
2 040
0 4C8
CLR
8
2042
0 4CD
CLR
13
2044
04 CF
CLR
15
2 046
C120
MOV
aAD0X,4 R4
HAS
X
D IS PL
2048
FCOO
2 04 A
Cl 60
MOV
3ADDY.5 R5
HAS
Y
DISPL
2 04C
FC 02
£04 E
6820
S
SACO X 3 A DO Y
2050
FCOO
2052
FC02
2054
0209
LI
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2058
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LI
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2 05 A
2200
2C5C
0203
LI
3, KEY
205E
FFFF
2060
0202
BEG I N
LI
2 .STATS
2062
2720


161
parameters. The only modifications in the program necessary
in the testing were introduced in,steps 3 and 4 due to the
nonunique communication between the two modules.
The program development and debugging took approxi
mately five months. Although some preliminary tests were
done with synthetic data, most of the testing was accom
plished with segments of abnormal EEG's from 4 patients.
One question frequently asked was, how can the
system's software be fully tested? Test by induction gives
promising results for a class of programs (Anderson, 1979).
However, when the program flow is data dependent, induction
fails. Alternatively, extensive testing of the program with
real data seems the only possible way. After 100 hours of
data analysis no anomalies due to programming errors were
detected, but it is felt that this point is open-ended.
Other testing problems drew more attention. An impor
tant one was computation time. Since the program has inde
pendent loops of different lengths, only the longest one
was measured. The longest loop is the statistics genera
tion after the recognition of end of seizure. The following
approach was taken: The program is interrupted when con
trol is in the waiting loop in the FILTER program. There
fore, a mask for PC can be incorporated in the interrupt
handler, such that it would return control to the monitor
when PC is different from the mask. At the end of SZURE,
another waiting loop was established including an increment
instruction. As expected, at the end of the first seizure


249
143
142
144
145
14*
147
9
130
121
120
64
t4a
149
150
66
65
67
19
24
10
wc5m*wcufi-FtQArci-n*o.oa)t-wcu
4f:aMsCMPLXC6.r!,i4CRCT) 5
On 1a3 J*1.m
rCTc* CWCRH-PS C.n 1
rtCQ CllWCS(r)**M/TC
ACaCAB3fvCD'X5)
IF(AC.LF.TCO) GO TQ 142
tcuac
continue
DO 144 7*1,100
n *R XT£ (6 11 Oi TOr>
un 545 Tai,10
iPITE f6. 16)
.iRITfCb, 1465
rOHATCaoy,34HPL0T OP HTGM ASS FILTER
call plotfxo3itks,i oqi
KOsO
. 1 aO
K P a 1-
wITeC&,9)(0Zfn.T1M)
FOHMATttHfl.SOX,7HPZ,2Fl7.71
BKLAHaQ.O
WWTTF(6,44]
y*TT£C6,1301
FUf1AT(lP0.40Xf laH BHAOKATtC FACTORS)
AMAGl V
AnAG2 t!)3P7 ( I) i
Sf-
l+rOMjRifPZfn)
*CnN.JGfPZCTn
WHTTE6,1 20 3 AM AG 1(I) ,AMAG2CI)
FORMAT 1 HO, 4(1 X,2F 14. )
00 65 Mai. mo,
WCS <*ii #-ir,s CM) *T
Ok'aCMPLX U .0,0.0]
C*CM0L7Cn..7,' AM3rsxp!/.c;**o*coE7Pfnc)-i.) *k2*(ce*p(wc)1'1. 3***1
IF CMWIOW.tO.!] C-0 TO 14t>
DO 64 1*1 ;i
'CCEXP'V
hC)**3-C£vp(v.C) *CPZ(I3+C0UGCZm 3 )*Pzf I) *CQNJG(PZ(I)
A H a A H / (
3)3
SO to 150
00 149 t*1,4
AHaAH/(CEPf4C)-P7Cni
MAG fM]aAH
dWaCASSfAH].
IF(SH-aWLAfi]e,5,<,S,66
BHI A^sOW
CONTINUE
NHITE C 6 11 9 ] 8WL AS
UO 67 iiai mo
MAaMAGCMj'
amaG(m) ac,\ai ma) /omlap
PHASE(MlATAnCaImaGCMa)/REALHA)3
an 19 .HI, m
wRITtC 6,2 4)
FORMATClMO]
HRITECi.10)
FORMAT Cl HO, 3 O X, 72WPI.QT OF eJAnO PASS DIGITAL FILTER)
CALL PLOT fMCEiAMas,!OO)
iTTeC6,a4)
30 TO 500
£N0


115
filters, but the zero crossing analysis of the filtered
data is capable of distinguishing the in-band from out-of-
band signals. There is, however, reduced quantitative
knowledge about choosing the Q of fourth order systems as
a function of the center frequency and period window.
For the slow wave filter the bandwidth was made as
large as possible and still be able to attenuate conven
iently (at least 20 dB) the spike component of the pattern.
After testing different bandwidths, a 0.8-6 Hz window was
selected. The Q is 0.42. The spike filter bandwidth was
selected to provide a trade-off between using most of the
spike energy and at the same time attenuate considerable
muscle activity. The best upper corner frequency was
thought 25 Hz, so the bandwidth was set 10-25 Hz, yielding
a Q of 1.* Fourth order filters were utilized, and the
ripple in-band was set at 15 percent, roughly 1.4 dB. The
ripple was selected as high as possible to increase the
out-of-band attenuation rate as (1-5) shows. The last
parameter to be selected is the sampling frequency. As a
straight zero crossing information is going to be employed
to determine the period of the filtered EEG, a resolution
of 10 percent was thought necessary to represent the spike
duration. This imposes a sampling frequency of 240 Hz
using (48). The slow wave bandpass magnification was
*The requirement of 40 Hz, maximum frequency, in
Smith (1974) regards slope measurements, which are not used
in this work.


197
group. The standard deviations for the half period of the
slow waves are comparable between the two groups.
The group of classical PM patients displays the
smallest repetition rate, while the PM variant possesses
the longest repetition rates. Repetition rate does not
seem to be connected by any strict rule with the half period
of the waves measured between valley and peak. For
instance, patients #12 and #5 have a longer half period but
smaller repetition rate when compared to patient #7. Fur
thermore, for the PM variant, the half period measure is
comparable to the classical patterns. These facts may
indicate that the recruiting rate and the slow wave genera
tion are independent processes.
About the delay, spike-slow wave, it should be pointed
out that it is the parameter that deserves less confidence
because, in the way it is measured, it is sensitive to
desynchronization of the pattern. This fact is shown by
the big values of the variance during seizure.
As expected, the variances for the amplitude parameters
are much higher than for the period measures. This clearly
points to the superiority of period measures as the leading
parameters for PM detection. The filtered spike amplitude
is smaller than the filtered slow wave amplitude, except
for patient #7, who displays a higher spike for the first
two sessions. Both amplitudes are fairly constant from
session to session, except for patient #5-2 (technician
changed gain in the middle of recording?).


76
case of two's complement truncation and the canonical
second order structure. Parker and Hess (1971) showed that
the occurrence of limit cycles can occur in the horizon
tally hatched region of the triangle shown in Fig. 7. The
cross hatched region is the stability region (Claasen, et al.,
1976). Simulations on digital computers have shown that no
limit cycles occur in the remaining region inside the tri
angle. Probably more important is to have an idea on the
bound of the amplitude of the limit cycle. The absolute
bound on the amplitude of a limit cycle of any frequency is
given by
D<0 or D>0 and 2/D<|c|
1
J
D>0 and D(2//D-1)<|C|<2/D
1
D>0 and |C|<2D(2/D-1)2
(38)
I < ,
11 max <
i-|c|+|d|
(1-/D)
i/D
k (1D)/1-C/4D
for complex roots (Peled, 1976). This bound is too pessi
mistic, and so the RMS bound is usually preferred (Sand
berg & Kaiser 1972) .. It is given by
1
1-|C|+D
1
(1-D) /l-C2/4D
D<0 or D>0 and
|C|>4D2/(1+D)
D>0 and |C|<4D2/(1+D)
(39)


sec
CNl
=J*
'
I ,
1 hour
Fig. 33a. Sz Duration Versus Time (#5-1)
i
200


182
pattern (the patient was dropped from the study due to
hepatic problems). The table results denote this fact.
The agreement in total time in patients #5 and #12 is also
good. In #7, the discrepancy in the total time of
seizure > 10 sec is due to the fact that this patient had a
characteristic seizure beginning: the EEG begins to show
periodic spiking with low amplitude slow waves. Only when
the pattern is of sufficient amplitude, the seizure is
scored by the system; the neurologist used the spike cri
teria for seizure initiation (Fig. 27a). In this group of
patients only three misses occurred in patient #5. The
seizures appeared in a low amplitude background (initial
stages of sleep) and were missed on account of their very
low amplitude. It is interesting to note that all the
false positive detections occurred in these three patients.
This is pure chance, but stresses the point that with an
automated system not only the EEG patterns count; the
system performance is also dependent upon artifacts.
The sorting of the seizures in the three PM variant
patients (3, 4, 16) was worse, but it seems that the
hypotheses underlying the PM model are a solid departing
point for good detection agreement. It is worth mentioning
that the large discrepancy in number and duration for
seizure > 10 sec in patients #3 and #4 was due to the fact
that these patients had very long seizures (up to 36 sec)
with frequent desynchronizations. They also displayed only
occasional spiking. For this reason it was common to end


058 sec
Fig. 36. Repetition Rate Versus Time (#12-3) 1.5 hour .
205


067 sec
Fig. 40c. R. Period Versus Duration (#5-3)
211


142
PEAK
Module that monitors the output of slow wave
filter, detects peaks and associated period and
amplitude requirements of the slow wave.
FILTER
Module that performs the two filtering functions
(at different fs). It is here that synchroniza
tion of program control and the sampling frequency
takes place.
SPIKE
Module that monitors the output of the spike fil
ter and decides about amplitude and period
requirements.
SZURE
Program that collects the data during seizure,
allows for desynchronization and decides end of
seizure.
STATIS
Module that evaluates the mean values and vari
ances of the detection parameters, e.g., amplitude
and period of spikes and slow wave, periodicity
and delay between spike and slow wave.
INTHAND
Program that sets the sampling frequency through
an interrupt.
CALIB
Module that sets the system thresholds. It is
independent of the rest of the detector.
The basic program flow is shown in the diagram of
Fig. 25. Besides showing the various modules, the inter
connections among modules are also displayed. Most of the
dependence among blocks is reduced to two, one input one
output point. However, PEAK and SPIKE have more than one


242
7) The attenuation (dB/octave) above cut-off is
A = 6nx+6(n-1)+20 log e (1-5)
where x=log2W, i.e., x=0 represents w=l. For e 20 log e<0, and so the attenuation increases with
the amount of in-band ripple.
Automated Design
Here, the automated procedure will be implemented by
relating the pole location of the function
H(w) = -1 (1-6)
Jl+eVtw)
with the frequency domain filter specifications. The square
root form ensures that all the poles are in the h left
half S plane. The poles of (6) are given by
T (w) = 1 (1-7)
11 £
or putting $=<{>^+<¡>2 in (2)
Tn(w) = cos ntf>^ cos hncj^-j sin ^ sin h^-
Therefore,
cos n cos hd) -j sin d> sin hd> = 2.
1 2 1 2 £
(1-8)