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Pedagogical Reforms of Digital Signal Processing Education

Permanent Link: http://ufdc.ufl.edu/UFE0024317/00001

Material Information

Title: Pedagogical Reforms of Digital Signal Processing Education
Physical Description: 1 online resource (52 p.)
Language: english
Creator: Christensen, Michael
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: adobe, captivate, digital, education, electrical, engineering, interactive, processing, signal
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The future of the engineering discipline is arguably predicated heavily upon appealing to the future generation, in all its sensibilities. The greatest burden in doing so, one might rightly believe, lies on the shoulders of the educators. In examining the causal means by which the profession arrived at such a state, one finds that the technical revolution, precipitated by global war, had, as its catalyst, institutions as expansive as the government itself to satisfy the demand for engineers, who, as a result of such an existential crisis, were taught predominantly theoretical underpinnings to address a finite purpose. By contrast, the modern engineer, having expanded upon this vision and adapted to an evolving society, is increasingly placed in the proverbial role of the worker who must don many hats: not solely a scientist, yet often an artist; not a businessperson alone, but neither financially naive; not always a representative, though frequently a collaborator. Inasmuch as change then serves as the only constancy in a global climate, therefore, the educational system - if it is to mimic the demands of the industry - is left with an inherent need for perpetual revitalization to remain relevant. This work aims to serve that end. Motivated by existing research in engineering education, an epistemological challenge is molded into the framework of the electrical engineer with emphasis on digital signal processing. In particular, it is investigated whether students are better served by a learning paradigm that tolerates and, when feasible, encourages error via a medium free of traditional adjudication. Through the creation of learning modules using the Adobe Captivate environment, a wide range of fundamental knowledge in signal processing is challenged within the confines of existing undergraduate courses. It is found that such an approach not only conforms to the research agenda outlined for the engineering educator, but also reflects an often neglected reality: that the student who is free to be creative, free to err, and free to self-correct is emblematic of the profession past, present, and future - to which he or she unwittingly aspire
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Michael Christensen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Taylor, Fred J.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024317:00001

Permanent Link: http://ufdc.ufl.edu/UFE0024317/00001

Material Information

Title: Pedagogical Reforms of Digital Signal Processing Education
Physical Description: 1 online resource (52 p.)
Language: english
Creator: Christensen, Michael
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2009

Subjects

Subjects / Keywords: adobe, captivate, digital, education, electrical, engineering, interactive, processing, signal
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: The future of the engineering discipline is arguably predicated heavily upon appealing to the future generation, in all its sensibilities. The greatest burden in doing so, one might rightly believe, lies on the shoulders of the educators. In examining the causal means by which the profession arrived at such a state, one finds that the technical revolution, precipitated by global war, had, as its catalyst, institutions as expansive as the government itself to satisfy the demand for engineers, who, as a result of such an existential crisis, were taught predominantly theoretical underpinnings to address a finite purpose. By contrast, the modern engineer, having expanded upon this vision and adapted to an evolving society, is increasingly placed in the proverbial role of the worker who must don many hats: not solely a scientist, yet often an artist; not a businessperson alone, but neither financially naive; not always a representative, though frequently a collaborator. Inasmuch as change then serves as the only constancy in a global climate, therefore, the educational system - if it is to mimic the demands of the industry - is left with an inherent need for perpetual revitalization to remain relevant. This work aims to serve that end. Motivated by existing research in engineering education, an epistemological challenge is molded into the framework of the electrical engineer with emphasis on digital signal processing. In particular, it is investigated whether students are better served by a learning paradigm that tolerates and, when feasible, encourages error via a medium free of traditional adjudication. Through the creation of learning modules using the Adobe Captivate environment, a wide range of fundamental knowledge in signal processing is challenged within the confines of existing undergraduate courses. It is found that such an approach not only conforms to the research agenda outlined for the engineering educator, but also reflects an often neglected reality: that the student who is free to be creative, free to err, and free to self-correct is emblematic of the profession past, present, and future - to which he or she unwittingly aspire
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Michael Christensen.
Thesis: Thesis (Ph.D.)--University of Florida, 2009.
Local: Adviser: Taylor, Fred J.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2009
System ID: UFE0024317:00001


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PEDAGOGICAL R EFORMS OF DIGITAL SIGNAL PROCESSING EDUCATION By MICHAEL CHRISTENSEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2009 1

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2009 Michael Christensen 2

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To m y parents, for their unceasing dedication, exceptional example, and tireless love; and to those educators past and present for which I have had the fortune to be a spectator, for kindling an ardor of passion within me and always serving as a boundless source of inspiration 3

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ACKNOWL EDGMENTS With great appreciation for his passion for im proving the state of e ngineering education, I thank my advisor, Dr. Fred Taylor, without whose generosity, humility, and patience this pursuit would have never proven possible. I am indebt ed moreover to Mr. Jim Kurtz for his invaluable insight and professionalism duri ng my time as a research engi neer, whose perspective on the engineering process and whose a ppreciation for the delicacy of ma nagement have served as a model to which I aspire. I finally recognize a ll of those whose unmitigated love and support I have received over the years; I only hope I have proven able to reciproc ate it in as pristine a fashion as I received it. 4

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TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF FIGURES.........................................................................................................................7 ABSTRACT.....................................................................................................................................8 CHAPTER 1 THE STATE OF ENGINEERING.........................................................................................10 Obstacles of the Past.......................................................................................................... .....10 Challenges in the Present...................................................................................................... ..11 2 THE POSITION OF THE ENGINEERING EDUCATOR....................................................14 Research in Engineering Education........................................................................................14 Educational Research and Di gital Signal Processing.............................................................17 3 DECISION-ORIENTED LEARNING...................................................................................18 An Argument Favoring Error.................................................................................................18 Filter Design Learning Modules.............................................................................................20 Finite Impulse Response Module....................................................................................21 Infinite Impulse Response Module..................................................................................23 Digital Signal Processing Module..........................................................................................25 Hardware Decisions.........................................................................................................26 Clock Division.................................................................................................................27 Processing Timeline and Device Selection.....................................................................28 Software Decisions..........................................................................................................29 Module Conclusion.........................................................................................................30 4 ASSESSMENT................................................................................................................... ....36 Existing Assessment Methods................................................................................................36 Employed Testing Methodologies..........................................................................................36 Testing with Introductory Undergraduates......................................................................37 Testing question and solution...................................................................................38 Preliminary testing results........................................................................................39 Testing with Senior Undergraduates...............................................................................41 Digital signal processing modul e test questions and solution..................................41 Digital signal processing module testing results......................................................43 Filter design modules questions and answers..........................................................44 Filter design modules testing results........................................................................45 Conclusions.............................................................................................................................46 5

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REFERENCES ..............................................................................................................................48 BIOGRAPHICAL SKETCH.........................................................................................................52 6

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LIST OF FI GURES Figure page 3-1 Filter design module transponder block diagram...............................................................31 3-2 Filter design module re solution clarification.....................................................................31 3-3 Illustration of out -of-band tone jammer.............................................................................32 3-4 FIR module timing calculations.........................................................................................32 3-5 Broadband jammer illustration..........................................................................................33 3-6 Matlab full-motion video capture......................................................................................33 3-7 Panoramic sensor model....................................................................................................3 4 3-8 DSP processor selection.................................................................................................... .34 3-9 Implementation with high strength, periodic data.............................................................35 4-1 Fall 2008 cumulative testing results..................................................................................47 7

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Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy PEDAGOGICAL REFORMS OF DIGITAL SIGNAL PROCESSING EDUCATION By Michael Christensen May 2009 Chair: Fred Taylor Major: Electrical Engineering The future of the engineering discipline is arguably predicated heav ily upon appealing to the future generation, in all its sensibilities. The great est burden in doing so, one might rightly believe, lies on the shoulders of the educators. In examining the causal means by which the profession arrived at such a state, one finds that the technical revolution, precipitated by global war, had, as its catalyst, institutions as expans ive as the government itself to satisfy the demand for engineers, who, as a result of such an existe ntial crisis, were taught predominantly theoretical underpinnings to address a finite purpose. By contrast, the modern engineer, having expanded upon this vision and adapted to an evolving societ y, is increasingly placed in the proverbial role of the worker who must don many hats: not sole ly a scientist, yet of ten an artist; not a businessperson alone, but neither financially naive; not always a representative, though frequently a collaborator. Inasmuch as change then serves as the only constancy in a global climate, therefore, the educational system if it is to mimic the demands of the industry is left with an inherent need for perpetua l revitalization to remain relevant. This work aims to serve that end. Motivated by existing research in engineering education, an epistemological challenge is molded into the framework of the el ectrical engineer with emphasis on digital signal processing. In particul ar, it is investigated whether students are better 8

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9 served by a learning paradigm that tolerates and, when feasible, encourag es error via a medium free of traditional adjudication. Through the creation of lear ning modules using the Adobe Captivate environment, a wide range of f undamental knowledge in signal processing is challenged within the confines of existing undergraduate courses. It is found that such an approach not only conforms to the research ag enda outlined for the en gineering educator, but also reflects an often neglected reality: that the stude nt who is free to be creative, free to err, and free to self-correct is emblematic of the profession past, present, and future to which he or she unwittingly aspires.

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CHAP TER 1 THE STATE OF ENGINEERING Obstacles of the Past Though the role of the engineer has expanded as a function of socioeconomic progress and technological innovation over time, many of its overarching princi ples have been preserved. Beyond the commonly perceived sense of civil service and technical sophistication, the discipline of engineering has differed notably from pure science and mathematics in its end objective. The process of design, though rooted in the scientific method and often requiring a mathematical basis, has proven to be characterize d ultimately as an art in its own right. Whether through the nuance of approximation or the motiva tion for abstraction, the engineer has always been implicitly tasked with framing such inte llectual pursuits relative to some element of the common good be it local, na tional, or global in an effort to balance desire with capability. For the engineer of generations past, this reality has been well captured through the prism of global conflict. During the Cold War, for ex ample, the perception of existential threat was raised to a sufficient degree to warrant significant governmental infl uence. As described in [1], feats such as the launch of Sputnik I placed Am erican technological prowess in question, leading to federal intervention through legislation such as the National Defense Education Act and through later incarnations like th e Perkins Federal Loan Program, resulting in nearly quadruple the number of terminal engineering degrees duri ng the height of tensions between the United States and the Soviet Union. I ndeed, by this metric, provocative un certainties such as the nuclear arms race and mutually assured destruction were in fact a boon to the engineering profession. Similar contextual descriptions arise in exam ination of electronic advancements during World War II, including modern radar systems [2], el ectronic countermeasures, communication theory 10

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[3], and the funda mentals of signal processi ng that serve as the canvas for pedagogical development. Though war serves as an excellent example of the advancement of engineering, the educational philosophy surrounding the profession has, until recently and irrespective of the state of international crisis, remained monolithic and homogeneous. In its inception, engineering was treated as an apprenticeship in most countries, with the United States being one of few sovereign powers to delegate its resources to engineeri ng through the traditional university system by way of legislation like the Mo rrill Act [4]. More poignant yet, th is description brought with it a broad and impacting implication: the engineering curr iculum was to serve, in either model, as inherently and intentionally inco mplete. All the while, left unfi nished, pedagogical models were not a documented focus; the aforementioned disrup tive technologies and the need for education of the highest caliber meant the student was tasked with a focus on the theoretical truth of a now practical reality. Questions of how such indivi duals learned or what best facilitated their learning were trumped by the discrete sensibility of what, according to the climate of the time, was needed to be known. As such, the now tr aditional pedagogical methods introduced and reinforced during this era, namely instruction by lecture and reference to text, still linger in the consciousness of student and educator alike, a nd only now is the profe ssion as a whole gaining insight into the conseque nces of those decisions. Challenges in the Present In the present time, the engineering profe ssion finds itself tasked with a multitude of responsibilities, not the least of which, one might argue, is the recapture of the identity to which it once laid claim. Though a persistent engagement in global conflict remains a source for innovation, the urgency to respond to it has yet to be received by the profession at large in the same fashion as the past; no archetypal techni cal adversary has arisen within the national 11

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consciousness, nor has any prototyp ical figure carried the p roverbi al banner of the engineering philosophy, which, in so doing, might galvanize a resolve within the populace for action. Indeed, the urgency of the modern generation is not fueled by an ex istential threat, but rather, as noted in [5], by an urgency for reform, stemming from a global marketplace and from which the populace of engineering is largely unaware. In that respect, the American educational syst em faces an uphill battle both in recruitment and retention. The graduation of engineers has maintained a progressive decline since the end of the Cold War, with recent studies [6] indicating th at more than half of all engineering students fail to complete their undergraduate curriculum and that the enrollment of women has declined systematically in each of the la st ten years [7]. Governmentally funded reports [8] indicated the graduation of 70,000 engineers within the United States in 2004. By contrast, though common knowledge within the field has sugg ested an increase in the number of individuals educated in foreign institutions, research [9] shows that the gap is in fact smaller than once thought between the United States and emerging technological super powers like China, India, and South Korea. Graduates in the latter na tions, according to such studies [8 ], reach the hundreds of thousands, and statistics such as these do gain public edito rial attention [10]. The contention regularly made within such literature is that the prohi bitive American sociopolitical climate and improved economic conditions abroad are largel y the cause for such convergence. It is no doubt fair to ask, therefore, what th e profession has done to curb this trend. Though there is an agreement that marketing to the younger generation is necessary [11] and that doing so as early as middle school [12] or within the early collegi ate developmental cycle [13] is ultimately profitable, the scope of the problem r eaches beyond any singular institution to tackle. Retrospective remarks from leading educators [5] unequivocally assert that governmentally 12

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13 funded efforts have been studied to death by agencies like the National Research Council, the National Science Foundation, and the American So ciety for Engineering Education. According to such far-reaching groups, the complication comes not with an ignorance of what to do, but rather with a failure to do it. Instead of a m odel of leadership [14], prominent figures in the process have observed a blas reaction to the si tuation. The synopsis fr om [5] summarizes the challenge: ... when talking with individual faculty member s, I sense a pervasive attitude that the system ain't broke, that it does not need to be fixed/changed. This attitude is not a resistance to change, but rather a sense of what we're doing is good, therefore it doesn't need to be changed. Framed another way, no external agent has b een present of sufficient influence as the government in previous decades [1] to induce an incentive to change, nor has a movement within the collegiate profession arisen to mandate it. In fact, despite periods of si gnificant growth [15], major fundi ng institutions such as the National Institutes of Health have not even had th eir financial repositories keep with the rate of inflation [1]. To address these symptoms, arguments have been presented [4] both for and against the need for faculty to have an expe riential, industrial basi s for their academic philosophy. Doing so, it is argue d, contributes to a nd partially validates their educational identity and entices the industria l sector to maintain a symbiotic relationship with the academic system. Since teaching responsibilities traditi onally only compose one facet of a professors obligations, one is left to wonder how these al arming situations will be addressed, and moreover by whom. It is with recogniti on of addressing this challenge that the research field of engineering education has emerged.

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CHAP TER 2 THE POSITION OF THE ENGINEERING EDUCATOR Research in Engineering Education Motivated by decades of research in e ducational psychology, the research field of engineering education currently exists in its formal infancy, spearheaded largely by the American Society for Engineering Education (ASEE) and its attendant publications. As discussed in [16], the agenda for this field has been compartmentalized into five major areas of investigation. The first field of engineering epistemology seeks to quantify the body of knowledge needed by the engineer, recognizing it s time-varying structure. Closely related, studies in engineering learning mechanisms focus on the technical repert oire that is developed to conduct oneself as a life-long engineer. A third area of engineering learning systems examines the means, environments, and distribution methods by which engineering is gained. In so doing, a fourth area of diversity and inclusiveness tackles the challenges of fusing these concepts within a global framework, both for the purposes of equity and utility. Finally, engineering assessment addresses the testing criteria and measurements by which engineering knowledge is gauged. Though all five of these topics are coupled to one another, metrics in each area have been developed, and methods for conducti ng rigorous research [17] appli cable to all such areas have aided in galvanizing the discipline. Since most educational research techniques to date have employed some novel element within existing coursework, whet her by the tacit or explicit de viation from traditional pedagogy, further seminal research [18-19] has revealed usef ul approaches in the de velopment of curricula. Examination of educational coalitions funde d by the National Science Foundation illustrated a systematic process by which success and produc tivity could be measured. Beyond initial development, the willingness to lead programs and implement them in a modular manner proved 14

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greatly beneficial in con vincing fellow faculty to follow suit. Development alone, however, fostered stagnation, resulting in the need for intrinsic mechanics to promote and retain utility. Though this description is arguably general, the spirit of its st ructure is a reflection of the challenge currently within the pe dagogical environment and has se rved as a motivational source for this research. That having been stated, nu merous transcendent challenges remain for the general engineering educator. While the tools of how people learn in pr e-collegiate levels have been well developed and continue to serve as a corner stone to ongoing research [20-21], the vision for the engineer of upcoming decades [11] is influen ced by the proliferation of technology within the classroom, whether as an intende d and independent inj ection of pedagogy or as a response to its embrace within the general culture of which stude nts are a part. The institution of student interactivity with technology has become increasingly commonplace and, at least within electrical engineering, an embe dded staple of the curriculum [ 22-23]. For the signal processing student in particular, programming environments such as Matlab continue to serve as an invaluable resource for the visualization and co mputation of tasks once deemed infeasible in previous generations of instruction. The capacity to support fluency in such topics, however, is often at odds with the limited time available to satisfy curricular expectations for a given course. As of the time of this research, the univers ity system as a whole, whether influenced by accreditation or industrial committee, has not uniformly accepted the burden to introduce support for such types of programmatic proficiency by way of courses serving solely that end. Nonetheless, the demand for technology in the classroom remains paramount, along with assurances that its inclusion is not subject to the traditional pitfalls of unconstrained media. 15

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To that end, the aforem entioned desire for th e modular deployment of learning systems is juxtaposed with the sobering real ity that students are both capable (oftentimes more so than their instructors) and willing to circum vent the spirit and intent of a learning system in favor of an improved result. Whether through exploitation with in programming objectives [24] or in efforts to circumvent the opportunity [25], the stark truth of academic honesty cannot be overlooked. Indeed, an alarming number of students within engineering have admitted to cheating during the course of their educat ion, and strong statistical correlati on has been found between academic dishonesty and other deleterious behaviors [26]. As a result, though the infusion of technology can yield extensive benefit, a subtle but necessary condition of security also applies. Educational systems deterred by or motivated to avoid these ch allenges oftentimes further consign the most representative elements of su ch pedagogical evolution to part icipation in so-called capstone sequences [27]. In so doing, many of the ultimate goals of the process have been shown to be lost in the proverbial ether, pointing to a larger reality. In that regard, though the technical hurdles aris ing within such an educational overhaul can be significant, fundamental misc onceptions about the worth of given approaches are arguably more challenging to dispel. Technical expertise has proven time and again to be an insufficient measure of educational aptitude [20,28], and yet th e proverbial null hypothesis to simply make coursework less challenging for students neither guarantees nor implies perceived benefit by the student. In fact, the contraposi tive is also a myth warranting dismissal: demanding and extensive coursework, which readily translates in the parlan ce of a student to a difficult professor, does not in fact systematically translate to poor eval uation of the course or its administrator [29]. Moreover, recognizing disparities in learning styles between the educator and the student [30], whether as a result of generationa l gaps or personality differences can have an immediate impact 16

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on the m anner in which assessment is conducted [31] and ultimately can serve as a direct indicator of how likely a student is to be retained in the process [32]. Educational Research and Di gital Signal Processing Educators have shown themselves aware of thes e realities to varying degrees, and learning paradigms have been constructed accordingly to address weaknesses and enhance perceived benefits. In the context of engineering education, a nomenclature unto itself has been developed to describe such compositions [33-35], though all invoke some measure of problem solving. Indeed, educational media for digital signal proc essing (DSP) with this objective in mind have come in an array of forms. For example, th e development of summative assessment methods for enhancing proficiency with Matlab has been a focal point for prominent educators in signal processing [36], and the emergent prominence of Te xas Instruments devices has brought with it a marketable demand for educational efforts to aid in developing foundational and applicationbased expertise in DSP principles [37-41]. Howeve r, be it due to the relative infancy of the engineering education process or simply the ignorance to it, few w ithin electrical engineering or DSP in particular have attempted to frame such efforts in a manner from which a more general understanding can be derived. By contrast, this research seek s to expand upon the authors previous trials in signal processing educati on [42] and to posit a number of critical epistemological considerations. 17

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CHAP TER 3 DECISION-ORIENTED LEARNING An Argument Favoring Error Engineering has been often characterized as iterative, developmental, and responsive to unplanned shortcomings. In this way, though engineering designs become increasingly driven by detail, they are equally subject to an incr easing tolerance of and compensation for more catastrophic circumstances. When framed in this light, one might rightly argue that the decision process for the engineer is multi-faceted; ha ving an understanding of successful operation is conditioned as much upon knowledge of why alte rnative techniques are unsuccessful. Indeed, arguments have been made both within scien tific journals [43] a nd in the mainstream consciousness [44] that the grea test innovation stemming from sc ientific endeavor (of which engineering is a part) is contingent upon the nece ssity of creativity and the willingness to make mistakes. When pedagogy is framed in a pejorative academic tense, however, such opportunities are inextricab ly lost and the traditional summ ative assessments methods used no longer measure or reflect ones preparedness for a career, but rather merely the quality of recitation. Said more simply, the student who is without the expectation to make decisions and experience their consequences be they beneficial or detrimental is voi d of a critical element of the engineering process, without which their pedagogy is fundamentally incomplete. This belief has served principally as the motivation for this research, producing several operational objectives. For the D SP engineer in particular, this mandates the framing of realworld problems in a fashion that replicates a t ypical design condition. First, the deployment of these learning mechanisms, hencef orth referred to as modules, must be sufficiently accessible to the student at his or her current level of topical knowledge wh ile still challenging and expanding upon it. In so doing, they must moreover house suffi cient latitude to tolerate faults in the 18

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learning process and support rem edi ation prior to the completion of the effort. Finally, to ensure consistency and induce increased comfort with the activity, student exposition to such modules must occur with sufficient regularity. With these ideals in mind, investigation into available outlets for th is notion of decisionoriented learning exposed an additional constraint. Previous e fforts to engage students more directly [45-46] were met with hesitancy to participate with a traditional adjudicative figure. Believing this was at least in part a result of social inhibition and simu ltaneously recognizing the aforementioned need for the infusion of technology, focus turned to the use of software development as an equivalent means of communi cation. Previous efforts have been developed and assessed with respect to software [22, 36, 47-48] and a similar learning paradigm has been explored in other areas of engi neering [49], but such pursuits have largely relied on customdesigned systems to serve that explicit end. In examining alternatives with a wider appeal, the use of the Adobe Captivate development enviro nment for learning module creation demonstrated considerable potential profit. Used by industr ies for traditional trai ning exercises in the workplace and currently in its third version, the functional framework of the system lends itself to concoct a unique experience as a function of constrained options th rough the principle of branching logic. This is achieved on the appl ication level by publishing the Captivate design into one of several possible file formats, in cluding HTML, Shockwave Flash, and a standalone executable. In addition, the final product can be viewed at high reso lution while containing features like embedded audio and full-motion vi deo to support a particular illustrative task. Though developmental time for a given module is a direct function of the desired sophistication all modules for this research required no more than forty hours each to support narrative audio 19

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and video the learning curve for the use of Captivate is extre mely limited, aiding in the effort for future distribution to other faculty. To test the efficacy of the learning philos ophy as well as the modules themselves, three major topical objectives were pursued and summ arily introduced to stude nts enrolled in signal processing courses in the Departme nt of Electrical and Computer Engineering at the University of Florida [50]. In each module, the student is placed in a sc enario that requires them to participate in a fashion similar to that of a wo rking engineer. The modules challenge the student to make immediate use of the knowledge he or sh e has recently acquired in traditional lecture, examining topics in filter design and DSP hardware and software, motivated by discussions in [36, 38, 51]. Filter Design Learning Modules The devised scenario places the student in the position of the singular DSP engineer in a multidisciplinary team, working to design and implement a rudimentary transponder technology for a collection of unmanned aerial drones in a po tentially hostile environment. As shown in Figure 3-1, each drone is assumed to transmit a si nusoidal tone to a base controller at a given frequency and for a specified length of time. Data from multiple drones is collected and filtered at the controller. A Fast Four ier Transform (FFT) is performed on the filtered data, followed by tone detection and frequency shifting on each incoming signal for verification and security, which is viewed by the learner as a black box. Nonetheless, once comple te, a valid input tone then undergoes an Inverse FFT (IFFT) and amplif ication before being transmitted back to the drone. This process is repeated multiple time s to decrease the chance of false positives. To increase system complexity, the fictiv e team has been tasked with adequately suppressing a jammer in the filter ing phase to decrease the probabil ity of a false detection. This entire procedure is further encapsu lated in a real-time constraint to eliminate the possibility for 20

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input overflow. W ith this information in ha nd, individual learning modules are provided to students that address specific design challenges, first with a finite impulse response (FIR) approach. Finite Impulse Response Module The first module begins by addressing sample rate restrictions as a function of the bandwidth limit indicated. Four options are provid ed: an aliased sample rate, critical sampling, extreme oversampling, and satisfactory oversampli ng. In the event students respond with any of the first three conditions, the module branches off to a remediation phase in which their choice is questioned. The critically sampled' case is given as an inadequate reason due to the need for a non-causal filter, and the extreme oversampling cas e is deemed improbable due to the real-time constraint, which the resultant filt er order would likely violate. In the event these reasons are not recognized, a final layer of remediation is provi ded, at which point the appropriate answer is given as a basis for continuation. Students are then tasked with managing a multitude of drones simultaneously. This is equivalently cast as selecting an FFT length in order to determine the satisfactory frequency resolution, much as in Figure 3-2. In contrast to the first decisi on layer, however, two ostensibly correct choices are provided along w ith two errant choices. Should an errant choice be selected, remediation is provided that indicat es either of the two remaining choices is satisfactory, with the student left to select one. This decision influences the br anch down which the remainder of the module will follow. To address potentially disruptive effects, the student is provided with the received jammer and signal powers. In so doing, they are tasked with designing a symmetric, linear phase FIR that will yield a specified signal-to-jammer ra tio for an out-of-band tone jammer, which is indicated to be sufficient for the tone detecti on process and is illustrated in Figure 3-3. An 21

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incorrect solution digresses into an explanation of frequency response and with it a graphical fra mework of the problem. With most critical design parameters in tow, the module then aims to simulate incremental collective knowledge gains (i.e. the time-elapsed design pr ocess) by injecting information about the system speed requirements via other member s of the project team as well as presumed personal research. Specificall y, quantitative timing estimates are given concerning the tone detection and amplification pro cesses as well as the documented benchmarks for FFT and IFFT processing, as shown in Figure 3-4. The student is then tasked with determining the amount of time remaining in the processing interval allotte d. Four options are onc e again provided, three being discrete values and th e fourth suggesting that insu fficient time is available. In this way, the prior decision concerning FFT length is amplified. Namely, a student who chose to use a longer length FFT, under the arguably vacuous assumption of the benefit to higher resolution, comes to find that th e process cannot be completed c oherently when accounting for the resultant increase to delay, whereas the stude nt selecting a satisfactor y but shorter length can in fact succeed. Should a student not acquire su ch an observation or alternatively select an inappropriate estimate of headroom, remedia tion is once again provide d to demonstrate the contributing factors to the timeline. The module then concludes by reinforcing the ma jor themes of the exercise and extending them to the working environment. Indeed, thou gh the student was in some sense led blind down a portion of the proverbial path, th is is indicative of an engine ering design which either is evolving or ill-defined, both of which occur in pr actice and are representative of the incremental and iterative process. Hints are then given concerning the next m odule, which aims to tackle the problem in a new light. 22

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Infinite Impulse Response Module Once studen ts have received preliminary in struction on IIR systems through traditional pedagogical means, the second module in the course is deployed. In it, several notable changes are made to the design plan to reflect discussions within the team and th e contract supervisor. Specifically, the concept of the jamming system is revisited, wherein the argument is made (by proxy) that a broadband jammer would be more proba bilistically effective to combat drone tones at presumably unknown frequencies, particularly t hose potentially within the filter pass band, as illustrated in Figure 3-5. Cognizant that a pow er-limited jamming system will be inhibited by increased operational bandwidth, the proposition is put forth that each drone could utilize a larger frequency range while simultaneously transmitting side band tones as a primitive countermeasure. In so doing, should the jammer, though described as broad band, in fact act more like a pulse across the chosen range, then su ch side bands could produce an artificial (i.e. desired) hit without disrupting communication. From this idea the module expands. The student is reminded that the choices made and information provided in the previous module impact the current condition. Specificall y, timing estimates for the black boxes were conditioned on specified sampling rate s and lengths, with a change to rate likely having a larger impact than a change to length. Therefore, ha ving to assume an invariant sample rate, the student is tasked with select ing an operational bandwidth and sideband spacing the latter equivalent to a message frequency that will give the jammer the greatest challenge. As this is achieved whenever adjacent side bands overlap, two seemingly suita ble choices are provided, one utilizing the entire unaliased ba ndwidth and one that does not, al ong with two incorrect choices. Should a student make an erroneous choice, the decision conditions are outlined in greater detail and only legitimate options are provided. 23

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W ith a selection in place, the module then addresses how to combat the cumulative effects of the drone side bands. The argument is made th at such side band tones would ideally wish to be suppressed in the filter bloc k so that the tone detection, IF FT, and amplification processes do not receive unnecessary contributions. Moreov er, lower memory requirements would promote the compact design that the sponsor is seeking. To that end, and without mandating an explicit design technique, the student is left to determin e the minimum amount of memory that would be required to store the filter coefficients to achieve such suppression. Irrespective of the students deci sion, the module then breaks from the scenario mode of Captivate and switches to a training mode utiliz ing full-motion video recording. At such time, the narrator rehashes the probl em at hand and makes use of Matlab to illustrate the design challenge. The concept of an IIR comb (not ching) filter is introdu ced using the Filter Visualization Tool as a viable solution to the problem, as shown in Figure 3-6. Both plausible alternatives are addressed, for which it is demons trated that failing to use the whole unaliased bandwidth would result in an uns atisfactory design. In contrast making such use not only would prove viable, but also would simplify an IIR methodology to an FIR result. Moreover, the student is led to conclude that significant memory savings can be had by this approach due to the need to store only a small fraction of the redundant filter coefficients. Once complete, the student is returned to the more familiar scenario environment and left to continue the exercise. Having established a fixed resolution and sample rate, a final challenge is presented in the form of timing estimation. The student is faced with assessing the latency resulting from successive drone transmissions. This process beco mes feasible to calculate due to a constant group delay resulting from the filter simplification. As in previous instances, a student failing to 24

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select an appropriate estim ate is reminded a bout the relationship betw een frequency resolution and sample length and how it, along with the filter delay, impact the timing specification. The module concludes with a synopsis of what was learned. The concept of simplification through generalization is reinforced, and practic al applications of th e study are introduced, eliciting the similarities betw een the project description and technologies such as frequency modulation and spread spectrum techniques. Digital Signal Processing Module The third learning module aims to realize the ideals of digital signal processing by placing the student within the confines of a multidiscip linary team once again, but now with a more farreaching aim. The functional concepts of realtime signal processing and radar signal processing in particular are introduced unde r the guise of remote surveillance of endangered species. Students are introduced to the problem at large by eliciting the need from their manager for an end-to-end signal processing solution that can operat e within arctic climates in an effort to capture migratory patterns of creat ures otherwise elusive to humans. In view of the significant posed interest associated with the effort, the st udent is immediately task ed with developing both a suitable hardware platform as well as a robust detection methodology to support a panoramic sensor array. In the former case, considerations a bout price and mass production are put into the framework of the scenario wit hout further immediate elaborati on, while in the latter case the sensor architecture is illustrated identical to Figure 3-7. As shown, four sensors form the array, each sensor sweeping a quadrant (or swath) of space by way of four narrow, steered beams, which the student is told responds to the presence of irradiated energy. This process produces sixteen refined position estimates wi thin the circular viewing position. 25

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Hardw are Decisions Since the software is irrevocably conditioned upon the hardware, the student begins by a survey of the Texas Instruments High Performance series of DSPs in a manner consistent with what a working engineer would find by way of pr oduct guides, informative websites, and pricing charts as of December 2008. First, the C6474 is introduced as the top-of-the-line DSP and critical specifications such as its parallel proce ssor architecture and peripherals are advertised to potentially entice the student. At the same time, its limitations are exposed, namely in its lack of modularity and customization and, due to its nove lty, its particularly hi gh cost. Motivated by these shortcomings, a second processor, the C64 5x series, is introduced as being a compromise of many ideals. Though not as fast as the 6474 device, its numerous op tions are articulated, including a wide range of available memory sp aces, operating regions, and processor speeds. Because of such latitudes, however, the pric e remains competitive with the 6474, and only in mass production would significant fiscal benefits be possibly obs erved. To once again play on these pitfalls, the C641x is presen ted as the lowest e nd alternative that mi ght satisfy the design conditions. Citing its versatility to be comp etitive with the 645x in processor speed and operating environments, the only listed limita tion is in its fixed memory space. From these descriptions, the student is task ed, albeit naively, with making a preliminary selection of hardware. Should he or she sele ct the high performance 6474, the module branches off into a separate discussion based on how, due to a lack of multiple operating ranges, the 6474 would fail in an arctic climate. Should the stud ent attempt to reason prin cipally on the basis of cost and therefore select the C641x series, anot her branch is formed that performs a more detailed analysis of the claims to versatility. Indeed, for arctic clim ates, a maximum operating frequency of only 600 MHz is given as the only supported clock rate, which, when compared to the alternatives, proves less than allu ring. In either case, or if the student did initially select it, all 26

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discuss ions then return (albeit on independent pa ths) to the 645x series chip. Because of the need for low temperature outfitting, the estimated co st per unit of $300 is in fact more than even the high performance 6474, but in view of no other options, the student is led to believe that it is the best decision. With a general make of proce ssor selected, the modul e then branches to inform the student on the differences in product models, both in price and performance. Though both the 6454 and 6455 models use an internal 1 GHz clock, the 6455 doubles the amount of available internal memory and supports inter-processor communication by way of Serial RapidIO. In view of the limited conceptual framework of the software desi gn at this juncture in the design, no decision is required of the student at this stage and in stead business issues are placed into focus. Clock Division As a narrative interlude, the fictive manager in the scenario then asks the student to place his findings into a fiscal contex t, namely with projected memory and timing budgets. Indeed, a detection algorithm that produces numerous points of interest, though seemingly robust, could, in later stages, prove to be detrimen tal in cost due to the need fo r additional memory. With this reality placed in context and the sensor modality emphasized once more, the concept of array signal processing is introduced as a spatial-te mporal problem, for which the two-dimensional FFT is selected to serve as a worthwhile mechanism for potential species identification. The student is then steered to cons ider possible radix selections fo r the production of such FFTs by way of TI documentation, for which only power s of two and four are shown as supported. With a firm memory restriction of eight kiloby tes in place for each full scan of the field of view put in place to guarantee that the system can run for a significant duration without the need to purge its contents, the student is then left to estimate the data collection timeline. Specifically, he or she must select a an integer divisor of th e 1 GHz clock rate as a sampling rate that will 27

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allow the m aximum number of 16-bit samples to be collected within each region and within a two microsecond time frame. Should the student select an unsatisfactory divisor, separate remediation branches are introduced that explai n how such a memory budget per scan implies a 0.5 kB allocation per region, which, at two bytes per sample, implies a maximum of 256 possible samples. The remaining algebra is illustrat ed along with block diagrams from the TI documentation to reinforce the decision and the c onceptual operation of the system moreover, after which the processing timeline associated with the 2-D FFT is investigated in more detail. Processing Timeline and Device Selection Though the FFT mechanism ostensibly serves as a graphical means for recognition, the student is reminded that it alone cannot serve as an automated detection methodology. As a first blush response to this, the suggestion is presented that all elements within the 2-D FFT result could be compared to a static threshold to declare a point of interest. Being provided the instruction cycle length for comparisons and further restricting the proc essing sequences to be serial, the student is then aske d to estimate a timeline for both the collection and detection phases of the signal processing for the entire panoramic fi eld of view. Should a selection be made that challenges the expected response, the scenario branches into a discussion on the technique for calculating the 2-D FFT, ultimately converging upon a final estimate. A proverbial wrench is then thrown into the mix by asserting a subtle reality to the problem: not all detections will ultimately be of interest. All the while, a mandate has been put forth to operate the system interminably with transmission of relevant information each second. The student therefore is left to realize that some method of pruning is necessary, be it by an increase to the sophistication of the detection process itself or by a hard limit on the number of accepted detections. However, in so doing, the narra tion argues, all of the necessary criteria are in place to make an informed decision concerni ng a processor model, as shown in Figure 3-8. 28

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To that end, the student is asked to select a DSP that will satisfy the aforem entioned expectations while restricting detections to fi ve per swath (e.g. quadrant). Su ch inquiries are solicited by way of estimating the amount of remaining availabl e memory, with the notio nal specification of negative memory implying the need for a more robust processor (6455) instead of its inferior counterpart (6454). Errors made within this pe riod are afforded immediate remediation in view of the closure of the hardware topic. Software Decisions To address the implementation of the detection algorithm, the focus is then turned to the production of software algorithms in Matlab, with the aim that their ar chitecture would prove suitable for porting directly to a DSP. To test student knowledge of programming principles and their relation to the target development enviro nment, three unique implementations are compared and contrasted. In the first example, the implemen tation is flawed in that it fails to collect the maximum number for each region, but rather will select as many samples per region until the maximum is reached. In so doing, the possibility for failed detections increases based upon the concentration of information relative to the static threshold provided; data from the first swath processed could, by this faulty implementation, eliminate the inclusion of any subsequent detections. Should this reality fa il to be observed, the associated code is explained in detail to demonstrate its limitations. A second implementation brings into question the worth of a static threshold in the presence of sufficiently high st rength, periodic data generate d by random integer permutation, shown in Figure 3-9. The underlying consequen ce of such a circumstance, one might rightly argue, is the unnecessary e xpenditure of time associated with the discarding results that could be physically attributed to leakage or other deleteri ous effects. Even in the presence of ideal circumstances, phenomena such as bipedal and quadrupedal gait are able to induce significant 29

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Doppler shif ts when receiving irradiated energy as previously described. With these things in mind, the student is tasked at this layer of the scenario with estimating the number of discarded points of interest under the assumption of a now correctly working parsing algorithm. Unlike the first implementation making use of three-dimensi onal vectors, the second format utilizes the structure data type in Matlab al ong with an indexing system more akin to that of a target development environment such as C. As an inhibiting factor, however, internally supported algorithms for sorting are used to provide contrast. In this way, student competence is tested both programmatically and conceptually. With that, though remediation is provided for errant decisions, separate branches are nonetheless inst ituted to reinforce the subtleties described, principally to serve as a foundation for the radar signal processing module to follow. The final form of the detection algorithm mi mics the target environment most closely by separating the 2-D FFT functionality into individual steps. Furthermore, rather than making extensive use of dynamic vector nullification, iterative processes are ut ilized to illustrate the need for a more modular transfer of code. Though func tionally identical to the preceding form in both input and processing, the student is tasked with determining the e ffect of changes to the static threshold with regard to how ma ny quadrants are reviewed and what type of values are retained. Module Conclusion Due to the increased problem complexity relative to preceding modules, a summative discussion is instituted to conc lude the module, chiefly to elaborate more upon the idiosyncratic aspects of each Matlab implementation. Particul ar emphasis is placed upon demonstrating what types and kinds of functions are typically s upported within both the TI DSP and Matlab development environments, including variab le instantiation, two-dimensional vector concatenation, and element nullification. A salient point, however, is asserted to the student: the contrived scenario arguably does not act as a real-time system. This is motivated chiefly by the 30

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observation that the am ount of time to process data was well in excess of the time required to collect it. The implication of this reality is that observations would be temporally (and possibly spatially) discontinuous, which, when needing to observe instantaneous motion such as with endangered species, could prove ca tastrophic. With such a desc ription, the student is reminded of the necessity for clear problem definition above all else. Figure 3-1. Filter design module transponder block diagram. Figure 3-2. Filter design m odule resolution clarification. 31

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Figure 3-3. Illustration of out-of-band tone jammer. Figure 3-4. FIR module timing calculations. 32

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Figure 3-5. Broadband jammer illustration. Figure 3-6. Matlab full-motion video capture. 33

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Figure 3-7. Panoramic sensor model. Figure 3-8. DSP processor selection. 34

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Figure 3-9. Implementation with high strength, periodic data. 35

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CHAP TER 4 ASSESSMENT Existing Assessment Methods Traditional psychometric analysis is conditi oned upon a variety of f actors, all of which ostensibly serve to enhance objective sensibilities For example, to assess the efficacy of a particular technique, students are frequently pa rtitioned into two groups: one having access to the material in question and one using only trad itional pedagogical techni ques, the latter being described as a control group. In so doing, no as sumption is made on the worth or harm of the technique, and the effort serves to stratify populations while still being unified under identical methods of testing knowledge. Certain assumptions concerning the distri bution and stratification of these groups can indeed influence the types of conclusions that can be drawn, and natural statistical traits further impact th is reality, particularly in the representation of given populations. Indeed, adequately large populati ons are often necessary to sa tisfy well-known statistical convergence requirements, implying limitations in the sample space either require sophisticated techniques to interpolate or ex trapolate behavior, or otherwis e inconclusive results follow. Functionally similar procedures ar e maintained in medical experiments with the use of placebos for demographically diverse populations, and th ese methods are so pervasive as to be a commonly accepted practice. Nonetheless, thou gh additional tests can be made concerning correlation, causation, and belief in dichotom ous hypotheses, the existing framework and curricular offerings have shown to limit available approaches. Employed Testing Methodologies To that end, though the modules themselves we re developed in the sequence previously described, the structure and content of existi ng undergraduate course s in signal processing influenced the order and manner in which the modul es were distributed. Moreover, contrary to 36

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the authors intended m ethod of use, students were ultimately not required by their instructor to participate in these exercises and were info rmed during their lectures and associated announcements that involvement would be entirely optional. It therefore should be stated unequivocally that the results stemming from this effort, particularly attempts to measure the effectiveness of the modules them selves, are not necessarily reflec tions of the product itself, but rather of the mechanisms used to deliver it. To that end, though unintended, this investigation has revealed that the approach students take with respect not only to the notion of optional material but also to their part icipation in electronic pedagogy can be reliably and quantitatively shown to largely be an act of expedited guesswork. Whether this therefore serves as a reflection of the arguments made in preceding chapters th at unperceived stagnation and fettered creativity are at the root of the problem has not undergone the necessary level of sc ientific scrutiny, but adequate evidence has been collected to suggest and highlight the beli ef that regurgitation impacts a students capacity for abstraction, a nd reinforces the commonly held belief that students largely oblig e themselves only to that which is ma ndated to them. These effects were first made manifest with freshman and sophomor e students and its effects were exacerbated as students persisted in the curriculum. Testing with Introductory Undergraduates The Fall 2008 semester was used for the pur pose of initial screening of the modules themselves as well as their co rresponding assessment techniques. A section of EEL3135 (Signal and Systems) under the administration of Dr. Fred Taylor was provided as a sample population. Within such a course, the typical student has ha d no previous engineering coursework and is only assumed to have gained the requisite mathematical repertoire to analyze the critical aspects of linear systems. (Several enrolled students were found to be graduate students, presumably 37

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auditing the course; the ir perfor mance was omitted in subsequent analysis.) Because of this, only the FIR module was utilized for the purpose of assessment. After students had been introduced to the cr itical aspects of FFTs and FIR filters, a testing technique was devised that would be of sufficient generality to be solved by a student using only material obtained through traditional pe dagogical means, yet of sufficient specificity as to benefit from the inclusion of the learni ng module. Through the comparison of performance on the testing material both prio r to and after the distribution of the module, the goal was to assess the difficulty of the problem itself as well as the learning modul e for students with the experience cited. Testing question and solution To that end, on 13 October, a single pre-test question was provided to students to be completed via the UF Learning Supp ort Services assessment software prior to the next lecture of 15 October 2008. The question was as follows: Consider a DSP which receives data from 5 unique analog inputs simultaneously. Each input has an Analog-to-Digital Converter (ADC) with a common user-selected sampling rate. If each input stream consists of 2048 ( buffered) samples that must all be filtered through a single 51st order symmetric, linear phase FIR within 10 milliseconds at the selected rate, what is the lowest nonzer o frequency that can be represented? Students were provided five opti ons for a response, four of which assessed understanding of filter mechanics and a fifth which allowed the student to select none of the answers provided. A maximum of one hour was afforded to solve the problem. With such a question, notional concepts of constant group delay and resolution are emphasized within the framework of a real-time requirement, much like the module itself. To answer the question, the student mu st first observe that since th e lowest nonzero frequency is equivalent to the frequency resolution, the lowest sampling rate that will achieve the timeline 38

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will se rve as the basis for the unaliased bandwidth. Division by the number of samples per input yields the desired resolution. The options provided for answers intend to address typical conceptual errors when attempting to solve problems of this type. Fo r example, the inclusion of one option would be correct in the case of parallel filter banks instea d of the serial one so described. Similarly, the inclusion of another option results from failing to ta ke into account the architecture of the filter, which reduces the group delay by a factor of two. The remaining response options were modifications or fusions of these themes to fo rce the student to discri minate between nearly equal choices. In similar form, a post-test was administer ed after the lecture of 15 October to be completed before the lecture of 17 October, with changes to the pre-test question in the number of buffered samples as well as the timeline restriction. Options were scaled accordingly and students were provided an identical period of time. Preliminary testing results A total of 42 students complete d the pre-test, with 15 answering correctly, an approximate 35.7% success rate. By contrast, 39 students completed the post-test with 12 answering correctly, an approximate 30.7% achievement. Though the -5% differential in and of itself proves concerning one could argue its statistica lly insignificance relative to random guessing a deeper challenge arose. Speci fically, a more thorough analysis of the pre-test and post-test results revealed an alarming oversight: many students (beyond the differential of three) did not participate in both examinations, requir ing their performan ce to be discarded. Of those students who participated in both te sts, the results were mixed. Since the LSS system monitors the amount of time a given a ssessment takes prior to submission, this time differential was used as a filtering agent. Sp ecifically, a student who spent an insignificant 39

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am ount of time (15 seconds or less) in either instance was taken to have guessed; the guessing contingent was one of three well-defined ones. The remaining two groups, all found to have spent a plausible amount of time solving the prob lem, either successfully answered the problem correctly on both occasions or did not. Of those who did not, however, there was no clear correlation found between time investment and accu racy of result with the exception of one student, who did not answer the pr e-testing question correctly but did so on the post-test while spending considerably le ss time doing the latter. Given the inherent inconclusive nature of these results, an alternative viewpoint was instituted to aid in later tes ting. Specifically, since the principal goal was to determine the difficulty of the question and the use of the modules, all other asse ssments for the semester were examined. As shown in Figure 4-1, the averag e student spent approxim ately 10.5 minutes on the pre-test compared to approximately 6 minutes on the post-test, but with marginally different results. At the same time, most instances of high performance were clustered toward short solution times. The interpretation of this observati on is partially obvious and partially insightful. To the former end, it stands to reason that th e student who knows how to solve a problem is more likely to do so more quickly than the problem he or she does not. At the same time, and to address the latter aspect, questions whose complexity rests principally in calculation and not conceptual formulation can inherently require more time to solve, of which several of the assessments shown are a part, as are problems in si milar introductory courses such as solid state electronics. As a result, though the question posed for students of this introductory course was posed once again to students of a senior unde rgraduate section for th e purpose of comparison, subsequent questions were framed around the intent to have solutions readily accessible within the time frame described. 40

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Testing w ith Senior Undergraduates The Spring 2009 semester was utilized for the remainder of testing within EEL4750C (Introduction to Digital Signal Pr ocessing), a technical elective taken by undergraduate students after having completed introductory courses in bo th continuous and discrete signal processing. The timeline for the distribution of the learning modules was influenced by the nature of the coverage within the course so as to ensure that all topics contained w ithin a partic ular module were covered in advance through established pe dagogical techniques. To that end, the third learning module covering DSP choices was distri buted first, with the remaining modules to follow. A total of 43 students were enrolled fo r the entirety of the exercises to be described. Digital signal processing modul e test questions and solution Immediately following a series of lectures on the FFT and its variants, a pre-test was distributed as a supplemental document during th e lecture of 18 February 2009 to be completed as a paper submission preceding the lecture of 20 February. Two questions were put forth as follows: (1) Suppose you wish to process two-dimensional da ta: one part spatial, one part temporal. Much to your surprise, the DSP available to you for processing supports 1-D FFTs of radix size R={2,3,4,5,8,16}. As a result, if an N-point 1-D FFT of radix R takes N log_R N clock cycles to compute, what is the fastes t that a 2-D FFT can be computed if you must collect at least 3100 temporal samples and 3800 spatial samples? (2) Youre trying to save pow er in completing calculations and are led to believe the power consumption will increase linearly wi th an increase to clock speed. The DSP requires 10 nW of power to calculate the 2-D FFT of (1) at its nominal 2.2 GHz clock rate. If such a clock can be divided down by any inte ger of your choosing, what is the fastest the 2-D FFT can be computed while requiring no more than 6 nW of power? The first question, beyond reinforcing the notional concepts of two-dimensional transforms, attempts to elicit knowledge about the use of zero padding to improve computational complexity while still recognizing the worth of atypical radixes. The inclusion of a radix table proved necessary to ensure that students were not left with solving a nonlinear optimization 41

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problem as a function of constrained sample length. In particular, though a radix-5 FFT is supported and would result in the least amount of zero padding of the temporal samples (e.g. 3125), the logarithmic complexity in fact decreases if the zero padding is extended to 4096 samples and a radix-16 FFT is used. Using th e same reasoning, the 3800 spatial samples are similarly zero padded to 4096 and a radix-16 FFT is again used. Recognizing additionally that the 2-D FFT is composed of successive invocations of 1-D FFTs, the complexity thus scales at double the square of the zero-padded length. As with the initial distribution of testing, five options were given for answers. The four errant choices were constructed to siphon potential conceptual flaws in the temporal and spatial lengths and radixes, respectivel y. For example, one choice made use of radix-5 and radix-2 FFTs for lengths of the nearest power of the radix (e.g. 3215 and 4096). Another used the most generic form (radix-2) for both dimensions, while another option used radix-5 and radix-16. A final option was generated as a bogus compilation of numbers. In providing these choices, the degree of conceptual error, outside of guesswork, is more readily manifest. To address the second question, the observati ons are arguably less profound. Due to a linear scaling of power consump tion with frequency, the 6 nW requirement relative to a 10 nW baseline implies that no greater than 60% of the clock frequency can be used. Since this value equates to 1.32 GHz, the clock operating at 2.2 GH z must be divided by two in order to produce a 1.1 GHz clock. The resultant speed is merely th e number of cycles calculated in the preceding question divided by this rate. To stratify responses once again, five options were provided. The first errant choice used a ra dix-5 and radix-16 FFT with a 1.1 GHz clock, while another mistakenly used the same radixes but for an undefined 1.32 GHz clock. A third option used the 42

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correct radixes but with an im proper clock frequency, and a final flawed choice made correct use of the clock frequency but using the aforementioned bogus calculation. Digital signal processing module testing results Students were presented with the two questions on 20 February 2009 to be due by 23 February in pre-test form, after which the learni ng modules were made available. From there, minor modifications were made to the relevant quantities as post-test questions, available on 2 March and due by 4 March. Nine students abstained from the process entirely. Using personal solution rates as a li tmus test for probable guessing (given a priori knowledge of the correct technique and answ er), the tests were examined both for accuracy as well as the speed with which such selections were made. T hough it is fair to argue th at students could have had exposure to the questions prio r to their participat ion, such an argument implicitly convicts the student of some measure of academic dishone sty, which the experiment would have been ill equipped to tackle. As such, t hose responses produced at a fast er rate were taken to suggest guesswork, and were lumped into categories of correct guessing and incorrect guessing. To account for the presumed effect of a faster solu tion rate as a function of prior exposure, a 20% attenuation was injected into the guessing measur e, making the solution speed that much faster; though this value is effectively heuristic, it proved to adequately delineate between cases in which students were probable to have randomly selected an option and those who simply could not solve the problem presented. The first question of the pre-test yielded an a dditional sixteen students not participating. Of those who did, eight produced th e correct answer for a mean response of 26.67%, but only two did so within a plausible time frame. To that end, the average time investment across all participating students was approximately 7.76 minut es, with seventeen students investing under the threshold of a minute of time. Similarly, for the second pre-test question, nineteen students 43

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did not participate, and of those rem aining w ho did, ten students answ ered correctly, but only one did so without being probabilis tically conditioned on guessing, be it due to time investment or errors in the previous question. For the post-test, a reduction to the seven students answered th e first question correctly, one previously having done so in the pre-test. Of those demonstrating improvement, four of the six had invested a plausible amount of time in their responses, with the remainder guessing. Students not falling into any of th ese descriptions produced inconclusive results as a function of their time investment or did not complete both activities. To that latte r end, four of the six students who correctly answered the first pre-te st question correctly in any form ultimately answered the post-test in correctly, and five of the six did th e same for the second question. By contrast, four of fourteen went fr om incorrect to correct for the fi rst question while four of eleven did so for the second question. Filter design modules questions and answers Distributed on 25 March 2009 to be due within three days, students were presented with several questions covering the topics of FIR and IIR filter design and an external reminder was produced concerning the optional nature of the events. The three questions addressed the concept of both tone and broadband jamming wit hout making direct use of such terminology. To that end, the pre-test qu estions were as follows: (1) Consider a DSP that recei ves data from five unique analog inputs simultaneously. Each has an Analog-to-Digital Converter (ADC) with a common user-selected sampling rate. If each input stream consists of 2048 (buf fered) samples, all of which must be filtered through a single 51st order symmetric, linear phase FIR while experiencing no more than ten millisecond latency at the selected rate, what is the lowest nonzero frequency that can be represented? (2) Suppose now a sinusoid operatin g out of the pass band of the filter interfered with one of the five analog inputs a nd it was known to have no more than 10 kilowatts of peak received power. For a maximally flat pass band, what minimum stop band attenuation 44

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would be re quired of the filter in (1) to ensure a 1 volt signal in the pass band was at least 20 dB above the out-of-band tone? (3) Now, instead of a single sinusoid interfer ing with one of the inputs, suppose there is a collection of sinusoids at each input having equal strength, with each sinusoid transmitted at a constant frequency spacing from one anot her across the whole una liased band width of the system. If the f ilter order is kept fixed at 51 but can be redesigned to produce a best effort of attenuating each of these tones, what is the minimum amount of memory required to store all five output data streams and the filter coefficients if all elements are stored as 16-bit values? The first question was identical to that provided to students in the previous semester in an effort to potentially glean measured improveme nt as a function of experience within the engineering curriculum. The second question addr essed the fundamental concepts of frequency response and units of measurement, wherein the effects of filter attenuation behave additively when measured in decibels. Students were gi ven options that either failed to adequately attenuate the disruptive tone or did not do so minimally relative to other choices. The third question was posed as the greatest challenge to students, requiring an ability to realize that the abstract description provided is representative of a comb filter. As such, memory savings can be had by intelligent programming, which is reflected in the learning modules themselves. With that, students were provided a combination of choices that include d and excluded both the number of inputs, the contributi on of filter coefficients to the memory budget, and the ability to interpret the results in the listed units of bytes. Filter design modules testing results Using personal solution rates and the Fa ll 2008 results as a metric for predicting guesswork, a total of 6.5 minutes we re allocated to the pre-test questions and a similar solution rate increase of 20% was afforded to the posttest. Moreover, the th ree questions provided signified three distinct levels of difficulty, implying that a stud ent was most probable to have 45

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solved the second question m ost eas ily, with the first question be ing of moderate difficulty, and the final question being the most challenging. Participation in these activities (as well as other non-experimental procedures) dwindled considerably by the time of dist ribution. For the pre-test, for ex ample, 29 of the 43 students did not participate. For the firs t question, two students answered correctly, with one student answering within an improbable time frame. The second question found four students answering correctly, with one doing so at a conceivably high rate. Four students al so answered the third question correctly, but one did so without any accuracy in preceding questions (while still investing plausible amounts of time) and two ot hers did so simply by a likely speedy guess. In the post-test, 23 students did not participate. Though six students answered the first question correctly, four did not do so within a plausible time frame. Six students also answered the second question correctly, with two likely to have guessed. A mere two students produced correct solutions to the final question, however, and neither did so within a credible time line. Both students answering the first question correctly initially failed to do so again; one in four also did for the second question and two of three fo r the third. Conversely, five of ten students who answered the first question in correctly were correct in the post-test, along with two of eight for the second question and one of nine for the third question. Conclusions As already suggested, the assessment of thes e modules comes with significant caveats. However, in recognition of limited participation and inconsistency in results, it is worthwhile to note that these habits are in fact consistent with other pedagogical ex aminations that were periodically given throug hout the semester in the same medium and with the same restrictions. In this regard, differentiation of the worth to th e learning modules relative to existing content is not possible by sheer virtue of such limitations but does speak to a la rger issue: students 46

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47 demonstrate either limited genuine dynamic problem solving capability or interest. In fact, the student body was shown to only consistently produce accurate solutions to problems when such problems were sufficiently similar to existing av ailable material, irrespective of the pervasive nature of concepts such as frequency response. In this regard, the argument of rapid production of answers as a result of preexisting understanding is reinforced. The converse of this hypothesis, however, is challenged by the results shown in this e ffort: expedient responses alone neither signify nor imply knowledge. Though th is fundamental observation is in no way surprising, the frequency with which it occurs suggests that policies mandating participation reduce the haphazard attitude with which circ umstances are approached. To that end, modifications to the manner in which this as sessment was conducted could conceivably have significant impact on the conclusions drawn from the effort itself. Figure 4-1. Fall 2008 cumula tive testing results.

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REFERENCES [1] Selingo, J., Gam e of Chance, ASEE Prism, Vol. 17, No. 5, 2008. [2] Buderi, R., The Invention That Changed the World: The Story of Radar from War to Peace, London: Abacus, Little, Brown, & Co., 1999. [3] Shannon, C., and W. Weaver, The Mathematical Theory of Communication, Urbana and Chicago: University of Illinois Press, 1963. [4] Gupta, M., Is Industrial E xperience Necessary for Teaching? IEEE Transactions on Education, Vol. 31, No. 1, 1988, pp. 9-20. [5] Wulf, W.A., The Urgency of Engineering Education Reform, Journal of SMET Education, Vol. 3, No. 3-4, 2002, pp. 3-9. [6] Fortenberry, N.L., J.F. Sullivan, P.N. Jordan, and D.W. Knight, Retention: Engineering Education Res earch Aids Instruction, Science, Vol. 317, No. 5842, 2007, pp. 11751176. [7] Loftus, M., Why Wont She Listen? ASEE Prism, Vol. 17, No. 3, 2007. [8] Committee on Science, Engineering, and Public Policy, Rising Above the Gathering Storm: Energizing and Employing Americ a for a Brighter Economic Future, Washington, D.C.: National Academies Press, 2007. [9] Gereffi, G., V. Wadhwa, B. Rissing, and R. Ong, Getting the Numbers Right: International Engineering Education in United States, China, and India, Journal of Engineering Education, Vol. 97, No. 1, 2008, pp. 13-25. [10] Lemonick, M., Are We Losing Our Edge? Time, February 5th, 2006. [11] National Academ y of Engineering, Educating the Engineer of 2020: Adapting Engineering Education to the New Century, Washington, DC: National Academies Press, 2005. [12] Cantrell, P., G. Peckan, A. Itani, and N. Velasquez-Bryant, The Effects of Engineering Modules on Student Learning in Middle School Science Classrooms, Journal of Engineering Education, Vol. 95, No. 4, 2006, pp. 301-309. [13] Qualters, D., T.C. Sheahan, E.J. Mason, D.S. Navick, and M. Dixon, Improving Learning in First-Year Engineering Course s through Interdiscipl inary Collaborative Assessment, Journal of Engineering Education, Vol. 97, No. 1, 2008, pp. 37-45. [14] Hairston, G., Progressive E ducators Must Lead, Not Follow, Journal of SMET Education, Vol. 1, No. 3, 2000, pp. 1-4. [15] Nature Editorial Board, A Crisis of Confidence, Nature, Vol. 457, p. 635. 48

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[16] Journal of Engineering Education Editori al Board, Special Repo rt: Research Agenda for the New Discipline of Engineering Education, Journal of Engineering Education, Vol. 95, No. 4, 2006, pp. 259-261. [17] Streveler, R., and K. Smith, Conduc ting Rigorous Research in Engineering Education, Journal of Engineering Education, Vol. 95, No. 2, 2006, pp. 103-105. [18] Borrego, M., Development of Engineering Education as a Rigorous Discipline: A Study of the Publication Patte rns of Four Coalitions, Journal of Engineering Education, Vol. 96, No. 1, 2007, pp. 5-18. [19] Clark, M.C., J. Froyd, P. Merton, and J. Richardson, The Evolution of Curricular Change Models Within the Foundation Coalition, Journal of Engineering Education, Vol. 93, No. 1, 2004, pp. 37-47 [20] Bransford, J., A. Brow n, and R. Cocking (Eds.), How People Learn: Brain, Mind, Experience, and School, Washington, D.C.: National Academies Press, 1999. [21] Wankat, P.C., Improving Engineeri ng and Technology Education by Applying What is Known About How People Learn, Journal of SMET Education, Vol. 3, No. 1-2, 2002, pp. 38. [22] Canizares, C., and Z.T. Faur, Advantages a nd Disadvantages of Using Various Computer Tools in Electri cal Engineering Courses, IEEE Transactions on Education, Vol. 40, No. 3, 1997, pp. 166-171. [23] Walker, M.B., and J.F. Donaldson, C ontinuing Engineering Education by Electronic Blackboard and Videotape: A Comparison of On-Campus and Off-Campus Student Performance, IEEE Transactions on Education, Vol. 32, No. 4, 1989, pp. 443-447. [24] Joy, M., and M. Luck, Plagi arism in Programming Assignments, IEEE Transactions on Education, Vol. 42, No. 2, 1999, pp. 129-133. [25] Parker, A., and J.O. Hamblen, Computer Algorithms for Plag iarism Detection, IEEE Transactions on Education, Vol. 32, No. 2, 1989, pp. 94-99. [26] Carpenter, D., T.S. Harding, C.J. Fi nelli, S.M. Montgomery, and H.J. Passow, Engineering Students Perceptions of and Attitudes Towards Cheating, Journal of Engineering Education, Vol. 95, No. 3, 2006, pp. 181-194. [27] Hoole, S.R.H., Engineering Edu cation, Design, and Senior Projects, IEEE Transactions on Education, Vol. 34, No. 2, 1991, pp. 193-198. [28] Borrego, M., Conceptual Difficulties Experienced by Trained Engineers Learning Educational Research Methods, Journal of Engineering Education, Vol. 96, No. 2, 2007, pp. 91-102. 49

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[29] Dee, K.C., Student Pe rceptions of High W orkloads are Not Associated with Poor Student Evaluations of Instructor Performance, Journal of Engineering Education Vol. 96, No. 1, 2007, pp. 69-78. [30] Rosati, P., R.K. Dean, and S.M. Rodman, A Study of the Relationship Between Students Learning Styles and Instructors Lecture Styles, IEEE Transactions on Education, Vol. 31, No. 3, 1988, pp. 208-212. [31] Vogt, C., Faculty as a Cr itical Juncture in Student Retention and Performance in Engineering Programs, Journal of Engineering Education, Vol. 97, No. 1, 2008, pp. 27-36. [32] Roselli, R., and S.P. Brophy, Experiences with Formative Assessment in Engineering Classrooms, Journal of Engineering Education, Vol. 95, No. 4., 2006, pp. 325-333. [33] Jiutso, S, and D. DiBasio, Experiential Learning Environments: Do They Prepare Our Students to be Self-Directed, Life-Long Learners? Journal of Engineering Education Vol. 95, No. 3, 2006, pp. 195-204. [34] Kumsaikaew, P., J. Jackman, and V.J. Dark, Task Relevant Information in Engineering Problem Solving, Journal of Engineering Education Vol. 95, No. 3, 2006, pp. 227-239. [35] Walls, M, The Undisc iplined Interdisciplinary Problem: PBL and the Expanding Limits of SMET Education, Journal of SMET Education, Vol. 1, No. 3, 2000, pp. 21-24. [36] McClellan, J., C.S. Burrus, A.V. Oppenhe im, T.W. Parks, R.W. Schafer, and H.W. Shuessler, Computer-Based Exercises for Signal Processing, Upper Saddle River, New Jersey: Prentice Hall, 1998. [37] Chassaing, R., Digital Signal Processing and App lications with the C6713 and C6416 DSK, Hoboken, New Jersey: Wiley & Sons, 2005. [38] Chassaing, R., DSP Applications Using C and the TMS320C6x DSK, New York: Wiley & Sons, 2002. [39] Kehtarnavaz, N ., and M. Keramat, DSP System Design Using the TMS320C6000, Upper Saddle River, New Jersey: Prentice Hall, 2001. [40] Gan, W., and S.M. K uo, Teaching DSP Software Development: From Design to Fixed-Point Implementations, IEEE Transactions on Education, Vol. 49, No. 1, 2006, pp. 122131. [41] Bose, T., A Digital Signal Proce ssing Laboratory for Undergraduates, IEEE Transactions on Education, Vol. 37, No. 3, 1994, pp. 243-246. 50

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51 [42] Christensen, M., R. Troche, and F. Ta ylor, ENGAGE: A DSP Le arning Paradigm for an Engineering Age, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2008, pp. 2629-2632. [43] Schwartz, M., The Importance of Stupidity in Scientific Research, Journal of Cell Science, Vol. 121, 2008, p. 1771. [44] Robinson, K., Do Schools Ki ll Creativity? 2006 TED Conference, http://www.ted.com/index.php/talks/ken_robins on_says_schools_ki ll_creativity.htm l Accessed February 2009. [45] Taylor, F., and J.D. Mellott, SP ECtra: A Signal Processing Engineering Curriculum, IEEE Transactions on Education, Vol. 39, No. 2, 1996, pp. 180-185. [46] Taylor, F., R. Frankel, and N. Nezi s, The InvestiGATOR : A Studio-Based DSP Learning Paradigm, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2004, pp.1013-1016. [47] Dahm, K., Interactiv e Simulation for Teaching Engineering Economics, Journal of STEM Education, Vol. 4, No. 3-4, 2003, pp. 1-4. [48] Roskowski, A.M., R.M. Felder, and L.G. Bullard, Student Use (and Non-Use) of Instructional Software, Journal of SMET Education, Vol. 2, No. 3-4, 2001, pp. 41-45. [49] Jawaharal, M, A. Shih, and P. Schr ader, Use of Scenario-Based Learning in Teaching Statics, Proceedings, ASEE Annual Conference and Exposition, American Society for Engineering Education, 2004. [50] Christensen, M., and F. Taylor, A Scenario-Based DSP Learning Study, Proceedings, 2009 IEEE Signal Processing Society 13th DSP Workshop & 5th SPE Workshop, Marco Island, FL, January 4-7. [51] Williams, A., and F. Taylor, Electronic Filter Design Handbook, New York: McGraw-Hill, 2006. .

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BIOGR APHICAL SKETCH Michael Christensen was born in 1982 in El Pa so, Texas. The younger of two children, he moved with his family to Florida in 1988 and has since lived in the cities of Lakeland and Gainesville while garnering his education. He received his Bachelor of Science (Magna cum Laude) and Master of Science in Electrical Engineering degrees in 2004 and 2005, respectively, from the University of Florida. From 2003 to 2005, he served as an undergraduate laboratory instructor in communication syst ems while dual enrolled in graduate school. From 2005 to 2006, he undertook research in radar signal processing sponsored by the Army Research Laboratory to develop and enhance machine lear ning algorithms for airborne mi nefield detection. He then allocated 2006 to 2007 exclusively to engineerin g education research, with numerous guest lectureships at the University of Florida focused on target envi ronment digital signal processing. Since then, he has simultaneously worked as a res earch engineer for the University of Florida in the development of end-to-end radar systems for nu merous defense agencies and a contributor to multiple undergraduate electrical engineering courses focused in signal processing. He has additionally contributed regularly both to signal processing a nd educational literature with publications in books, magazines, journals, and conferences. Since completing his degree, Michael has b een in negotiation with a host of defense agencies to offer his services in ra dar signal processing as an engineer. 52