1 Welcome to the 2014 CTSS Summer Workshop at Rose-Hulman Institute of TechnologyMario Simoni Rose-Hulman Maurice Aburdene Bucknell University Farrah Fayyaz Purdue University Signals 1

2 This is an outline of the whole workshopDay 1 Introduction (Mario) Collected Data What brought us to do this work Data from experiments (Farrah) Overview of conceptual learning (Farrah) What is a concept? Different theories Hands-on application-oriented activities (Mario and Maurice) Why do them? What’s happening at Bucknell and Rose-Hulman Introduction to the technology (Mario) Analog circuits Portable measurement equipment Day 2 Hands-on activites with the equipment (Mario) Lab 1 – Linearity and time-invariance (Day 1) Lab 2 – Periodic signals and DTMF tones Lab 3 – Basic filtering and the ECG Lab 4 – Filtering with 6th order circuits Lab 5 – Sampling Development of new activities (Everyone) Day 3 Presentation of new activities (Attendees) Review and assessment of the workshop (Everyone)

3 A special Thank You to all of our sponsorsThis workshop is supported by NSF Grant #

4 An Introduction to how we got started in this project and eventually came to be here.Mario Simoni Rose-Hulman Institute of Techonogy Department of Electrical and Computer Engineering

5 By the end of the quarter, we expect the students to understand at least some of the fundamental concepts By the end of the course, most students can correctly differentiate between the time and frequency domains, but they may not be able to correctly identify the period or the specific frequencies involved. This student did get it correct.

6 Here are some examples that illustrate the difficulties and misconceptions that students are facing.“since I obviously can’t convolve a sgn very well, I decided to do the transforms” [Got the transform correct to this point] “Nevermind, I’m going to use sgn”

7 This is the result of the next problem on the same exam from the same student.Given the spectrum below, find the corresponding time function using standard transforms and properties. The student was able to successfully recognize the Duality property and navigate through a problem with a greater number of more difficult steps. The difference is that Duality provides a procedure that can be momorized and applied in the same way each time. Successfully navigated Duality and solved a problem with more steps

8 Cumulative Withdraw and Fail data from for Rose-Hulman ECE students shows that Emag I and CTSS courses are most difficult. Use this slide to create a new slide. Freshman- Sophomore Junior 8 Cumulative data from Rose-Hulman Registrar

9 Discussion: What are the common threads between the introductory CTSS and EMAG courses?Use this slide to create a new slide. 9

10 We collected and are looking at a lot of other historical data in relation to ECE300 from Rose-Hulman during the time period of 2004 to 2012. Pre-Requisites Other ECE Courses Other Data Physics II EMAG I & II Tech Comm Physics III Dynamical Systems Cum GPA Diff Eq I DSP CTSS Concept Inv Diff Eq II Comm Sys Gender Intro Programming Digital Sys

11 Certainly the mathematics background contributes, but it’s not the only issue.As with n=218 in each group Bs with n=284 in each group Those students earning As in ece300 are earning As in all the other courses. What makes them good students? What can they do that other students cannot?

12 Students earning a C in ECE300 n=260 in each group

13 Students earning Ds and Fs in ECE300Ds with n=104 in each group Fs with n=96 in each group

14 We performed more detailed analysis of the data to determine if other factors skewed the resultsIs it one particular teacher? 8 different faculty taught over 10 years One faculty had no failures, which skewed the failure rate down not up Is it a particular textbook? At least 4 different textbooks were used Was it a particular group of students in a particular class? The failure rate is consistent from year to year Was a particular quarter in which they took the class worse than others? Seems to show a stronger correlation with GPA than the particular quarter Did the amount of time from the last math class affect the failure rate? The percentage of Fs actually declines with an increase in time, while the percentage of As increases

15 Are students failing because they aren’t doing the work or because the course is really more difficult? The Concept of a Learning Curve Performance Effort

16 Students were able to perform well in mathematical preparation but still perform poorly in the CTSS course and the EMAG Fields course

17 Student performance seems to be correlated more with GPA than other factorsPercentage in Population Quarter in Which CTSS Course was Taken

18 We have some hypotheses for why students struggle with CTSS materialProcedural Knowledge To solve this problem follow this procedure Substitute the delay value Pull constants out of the integral Change the integral to a step function Conceptual Knowledge To solve this problem conceptually, understand what is really happening

19 Performing experiments to better understand misconceptions This preliminary research has opened the door to further questions about this problem Performing experiments to better understand misconceptions Testing our hypothesis about conceptual learning using the concept inventory results Understanding other factors such as learning styles Can carefully designed laboratory experiments help to improve understanding What pedagogical techniques can steer students away from procedural learning and improve conceptual understanding

20 Farrah Fayyaz Purdue University School of Engineering EducationA description of qualitative experiments that we conducted to identify misconceptions and presentation of some preliminary results Farrah Fayyaz Purdue University School of Engineering Education

21 Research Questions MethodologyWe recently developed and conducted a qualitative experiment to identify common misconceptions and difficult content Research Questions What misconceptions do undergraduate electrical engineering students hold within Signals and Systems course content? How do these misconceptions differ after taking more courses that require pre-knowledge of these contents? How does the undergraduate electrical engineering students' conceptual understanding of the contents in Signals and Systems relate to their understanding of foundational mathematical concepts? Methodology Protocol Development Think-aloud individual interviews with students (N=19) Currently in the data analysis phase

22 Convolution and Multiplication Frequency and Time Preliminary analysis of the data has revealed some of the persistent misconceptions of undergraduate students with respect to CTSS content. Convolution and Multiplication Frequency and Time Aperiodic signals and their corresponding periodic signals Graphical challenges and misconceptions Mathematical challenges and misconceptions Confounding Terms Others

23 Convolution and MultiplicationStudents confuse multiplication with convolution because i) Convolution process involves multiplication, and ii) Convolution of two signals in one domain is multiplication in the other domain Examples of student responses: h(t) is from -1 to 1 and if we convolve x(t) with h(t) then y(t) will also be from -1 to 1.   If you convolve a triangular function with an impulse train, the result will be the product of two functions.   If we are convolving two signals in frequency domain, we will simply multiply them in the frequency domain.  

24 Frequency and Time Students find difficulty in explaining a frequency domain representation of a time domain function and vice versa. Students have trouble in looking at one domain and not think of the other domain simultaneously. Students are not very clear about the concept and limitations of Fourier analysis. Students rely more on mathematically finding Fourier series or transform rather than intuitively understanding the signal and its corresponding frequencies. Examples of student responses: Solved integral to find Fourier transform of 𝑑 𝑡 =𝑡 2 and got infinity in the answer. The participant got confused and kept checking their mathematical calculations to check what went wrong. I can mathematically prove the inverse relation between length of signal in time and its bandwidth but I cannot explain it otherwise. In Fourier transform table a delta function is impulse in time domain and 1 in frequency domain, I think it means that a delta function has no frequency as its Fourier transform has no ω in it. I honestly cannot think of how to find Fourier series of sin⁡( 𝜋 6 𝑡− 𝜋 6 ).

25 Aperiodic signals and their corresponding periodic signalsThe participants showed insufficient understanding of the relationship between the properties of an aperiodic signal and their corresponding periodic versions. Examples of student responses: If you make a signal periodic in time, its Fourier transform also becomes periodic with the same period. If you make a signal periodic, its Fourier transform becomes periodic due to superposition principle. I generally think if a signal is periodic in time domain, it is also periodic in frequency domain, just like if we have an impulse train

26 Graphical challenges and misconceptions­Students are not very comfortable with graphs and graphical analysis of signals. Examples of student responses: It would have been easier for me to convolve two signals if I had mathematical expressions instead of graphs. When plotting magnitude and phase of X(ω)=sin(πω), drew impulses for magnitude at ±π but drew phase as a constant pi/2 from -∞ to ∞. The integral of a rectangular function from -1 to 1 is a rectangle function from -1 to 1 and height 2. Convolving x(t) and h(t), tried mathematically and failed and then tried graphically and drew correct result. When asked why did not try graphically initially, the participant replied, I could not convolve by graphical method initially in 205 but after taking discrete it made more sense to me. I have taken communication too. I think repetition has made me understand it.

27 ­ Mathematical challenges and misconceptionsi) Student sometimes do unnecessary math and overcomplicate the problem at hand ii) Students make mathematical mistakes iii) Students fail to interpret a mathematical expression iv) Students fail to translate a signal in one representation (e.g., graphical) to its mathematical representation and vice versa. Examples of student responses: Fourier series is infinite summation and cosine and sine are infinite duration signals. There is no way I can find Fourier series of 𝑣(𝑡)= cos 𝑡+ 𝜋 sin⁡(7𝑡) using formula. When plotting magnitude and phase of X(ω)=sin(πω), drew impulses for magnitude at ±π but drew phase as a constant pi/2 from -∞ to ∞. The limits of integral to find Fourier transform of 𝑡 2 𝛿 𝑡−1 will be from 1 till π. 𝑧 𝑡 = 𝑡 2 𝛿 𝑡−1 exists only at t=1, so 𝑧 1 =1 and Fourier transform of 1 is 1.

28 ­Confounding Terms Sometimes students use certain concepts in a particular question that are correct in some other context but do not apply appropriately in the problem at hand. Examples of student responses: Impulse train is an impulse response Phase shift is time shift in frequency domain I know about how to apply superposition principle in circuits but I do not know how it can be applied in signals. Time-invariant means system has no memory as time does not affect much.

29 ­Others These are a few misconceptions that I am still struggling to fit in the categories already defined. Examples of student responses: Fourier series will just be discrete points of the Fourier transform Fourier series will be more precise than Fourier transform as you will be able to take certain points and build on them and sum them. If you have Fourier series of a periodic signal and you make it continuous, then that will be the Fourier transform of that periodic signal.

30 Wage et al. also describe what students perceived as the difficult concepts in signals and systems courses With regard to convolution: “I think it was because of the…I don’t want to say double integral…but I always say the concept of flipping and shifting, integrating two terms because really in calculus we used to integrated one term or just a straight double integral…and this required actually conceptualizing the shifting... as soon as it put visually that you were flipping and shifting then the integral made sense.” With regard to Fourier Transforms: “All of these symbols doesn’t really…doesn’t mean anything…and then you’re like ok…you look at them and you’re like I can do this there are only a couple of times you use them and you’re scratching your head because it doesn’t it’s.. it’s harder than it looks…and not I mean we spent a lot of time on it but just basic conceptual questions I had just weren’t answered. I tried to ask [the professor] and [the professor] did get the point across to me like I had this like glimmer of understanding and I just lost it.”

31 Wage et al. also indicated that student perceptions of the importance of topics could be a motivational factor

32 Farrah Fayyaz and Mario Simoni School of Engineering EducationAn overview of different learning theories that could help to explain causes of misconceptions Farrah Fayyaz and Mario Simoni Purdue University School of Engineering Education

33 First approach to find sources of difficulty was student learning style preferences, the Felder-Silverman Model. Converting to knowledge Active Doing Applying Discussing Reflective Thinking Reflecting Type of Information Sensing Facts/data Details Methods Intuitive Principles Generalizations Symbols Modality Preference Visual Pictures Diagrams Verbal Words Expression Progression of Thought Sequential Logical order Global Bits Intuitive leaps Use this slide to create a new slide. 33

34 Data from ILS for 732 Rose-Hulman ECE students from 2003-2012Active Sensory Sequential Visual Reflective Intuitive Global Verbal 34

35 Learning theory can provide a vocabulary and framework for discussing learning of abstract conceptsBloom’s Cognitive Taxonomy J. Pilgreen. taken June, 2013 B. Chapman. taken June, 2013

36 Deep Approach Surface Approach DefinitionExamine new facts and ideas critically, tie them into existing cognitive structures, and make links between ideas. Accept new facts and ideas uncritically and attempt to store them as isolated, unconnected items. Character-istics Look for meaning and central concepts. Relate new and previous knowledge. Link course content to real life. Rote learning of formulas Can’t identify principles from examples. Learn only for the exam Encouraged by Students Curiosity Determination Mentally engaged Confidence Only for degree Lack of academic focus Lack sufficient background Too high workload Cynical View High anxiety Encouraged by Faculty Bring out structure Plenty of time for concepts Confront misconceptions Active learning Assessments require thought and combine ideas Relate new material to previous Allow mistakes and reward effort Present series of unrelated facts Allow passive students Assess independent facts Cover material at expense of depth Excessive workload Discourage questions Too short of assessment cycle Houghton, Warren (2004) Engineering Subject Centre Guide: Learning and Teaching Theory for Engineering Academics. Loughborough: HEA Engineering Subject Centre

37 Discussion: Tie learning theories back to misconceptions

38 A Few conceptual change theories that may give some insight into some of the learning hurdlesOntological categorization [Chi (1992; 2008] Chi, M. T. H. (1992). Conceptual change within and across ontological categories: Examples from learning and discovery in science. Cognitive Models of Science Minnesota Studies in the Philosophy of Science, 15, Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. International handbook of research on conceptual change, p-prims, coordination classes, and knowledge in pieces [DiSessa (1993, 2008)] DiSessa, A. A. (1993). Toward an epistemology of physics. Cognition and instruction, 10(2-3), DiSessa, A. A. (2008). A bird’s-eye view of the “pieces” vs.“coherence” controversy (from the “pieces” side of the fence). International handbook of research on conceptual change, Framework theory [(Vosniadou & Vamvakoussi, 2006)] Vosniadou, S., & Vamvakoussi, X. (2006). Examining mathematics learning from a conceptual change point of view: Implications for the design of learning environments. Instructional psychology: Past, present and future trends. Sixteen essays in honour of Erik De Corte, Advanced mathematical thinking [Dreyfus (1991)] Dreyfus, T. (1991). Advanced mathematical thinking processes. Advanced mathematical thinking,

39 Ontological CategorizationConceptual change is the change in the categorical status of a concept Assigning correct conceptual category to a novel concept leads to conceptual change Assigning incorrect category (specially ontological) to a new concept leads to robust misconception

40 Is there a need to define categories in the subject matter?Continuous time or discrete time - Are the two ontological categories being mixed up in the presentation of various concepts Continuous frequency or discrete frequency – Hz represents cycles/sec or cycles/sample? Does this further any conceptual hurdles to understand discrete frequency Complex and real - Sinusoidal signals represented as complex exponentials, does that make them complex signals? 1. Graphical representation of discrete and continuous domains are same 2. At various places the continuous time signals are declared as discrete time signals without explanation 3. For ease of calculation, wherever necessary, discrete time domain is used as continuous time domain

41 Discussion: Do you see any misconceptions related to improper categorization.

42 diSessa describes the difference between experts and novices as the way we use phenomenological primitives (p-prims) Why is it hotter in the summer?

43 p-prims, coordination classes, and knowledge-in-piecesStudent’s prior knowledge conflicting with expert’s knowledge is not a misconception, but a phenomenological primitive (p-prim) knowledge invoked in an inappropriate context Inappropriate contextual use of p-prims leads to robust misconception Knowledge structure of a learner is fragmented Conceptual change occurs when the individual’s p-prims are re-contextualized Learning involves development of knowledge structures that consist of isolated or loosely linked p-prims into more coherent and integrated knowledge structure called coordination classes Readout strategy Causal net Readout strategies define the perceived elements that form the focus around which the system is interpreted. They are strateggies that are invoked when making observations and extracting information about a particular situation

44 Student misconceptions in signals and systems and their origins – Part II (Nasr R., Hall S., and Garik P., 2005)

45 Are there any potential p-prims furthering hurdles in learning?Time (clock - always continuous) Hz – cycles/sample or cycles/sec Periodic signals – infinite in length (electric current). What about discrete frequency?

46 Discussion: Do you see any misconceptions related to p-prim errors?

47 Framework theory Knowledge system of a person is a complex integration of numerous beliefs developed by interaction with physical, social, and cultural worlds around a person Conceptual learning becomes a problem when the person lacks initial compatible framework to add new knowledge in mind and is not even aware of the missing appropriate framework To conceptually learn concepts that conflict with well acquired everyday knowledge, the learner needs to be actively aware of his/her existing knowledge structure and the learner must be able to reassess his/her existing knowledge structure whenever required Example, radical re-structuring of the initial belief from everyday life about numbers is required to properly understand the concept of a rational number. 1. Being aware of one’s knowledge complies with the metacognition model of cognitive learning theory (Svinicki, 1999). 2. Ability to reassess the knowledge schema corresponds to structuring and restructuring of memory which complies with the early cognitive model of learning (Svinicki, 1999).

48 Discussion: Do you see any misconceptions related to lack of an initial framework?

49 Advanced mathematical thinkingStudents learn advanced mathematical concepts through reflection on mathematical activity Students’ failure to reflect on advanced mathematical concepts is the incomplete presentation of these concepts Abstract concepts can only be understood in terms of their relationship with other similar or different concepts, and hence, understanding these concepts require a mental ability to shift attention from the mathematical object themselves to the structure of their properties and relationships. A slight change in the structure of the problem or formula can completely block their mental processes In addition to creating a mental representation of a concept, learning an advanced mathematical concept requires an ability to mentally switch from one representation or formula of a concept to its other representation or formula. Learning an advanced mathematical concept requires an ability to mentally translate the mathematical concept in different contexts. This corresponds to the ability of a student to apply a mathematical concept to multiple problem statements. mathematics is created from a lot of abstractions and assumptions but teachers and mathematicians present mathematics to students in the refined form. This simplified presentation of otherwise complex and abstract mathematical concepts hinders the creation of mental processes required for advanced mathematical learning. This learning of mathematical concepts without mental processing can enable students to apply mathematical formulas in well-structured questions, but does not prepare them to reflect on mathematical activities. For example, applying a second-order, linear differential equation to an electric circuit problem requires students to translate the same quantities in the formula in the context of the differential equation as well as in the context of the electric circuits

50 Advanced mathematical thinking

51 Discussion: Do you see any misconceptions related to a lack of advanced mathematical thinking and reasoning?

52 Now that we have some idea of the misconceptions and the theories that might describe how they arise, how can we develop pedagogy to improve conceptual learning? Mario Simoni

53 Example: How can an understanding of the sources of difficulty and conceptual learning influence pedagogical practice? Nokes and Ross demonstrated that using examples to explain principles instead of principles to explain examples provided a more abstract understanding of a principle that could be applied to other contexts 1 Explain why the square wave shown above does not contain even harmonics. One paper suggests a couple of mechanisms to help students develop a deeper approach to learning. T. Nokes and B. Ross. Facilitating Conceptual Learning Through Analogy and Explanation. Physics Education Research Conference, Edited by L. Hsu, C. Henderson, and L. McCullough, pp. 7-12, 2007.

54 Using near-miss analogies can help students understand how the structure of a problem relates to variables. Using surface different problems helps students to determine which principle to apply. Near-miss Analogy Example 2 A Determine the value of A and τ that will make the fundamental frequency cosine have the same amplitude for each square wave. Surface Different Problem Example 2 Write an expression for the Fourier series coefficients for each signal

55 Discussion: Given all of this background information, why is the CTSS content so difficult for students? “It’s not the just the graphing, it’s not the just the math, it’s not just the experience… It’s using them all together.” Ruth Streveler, June 25, 2013 What do you think?

56 Given that we are going to be looking at hands-on activities for the remainder of the workshop, how should we think about them in relation to all of this learning theory?

57 Department of Electrical EngineeringWhat are we currently doing and advocating with regards to hands-on application oriented activities Mario Simoni Maurice Aburdene Bucknell University Department of Electrical Engineering

58 Wow! Linear Systems and Signal Processing is fun!58

59 Continuous-time signal processing is all about modeling what is happening in real systems.“#” button “1” button Talking about and modeling systems t=linspace(0,0.02,500); num1=cos(2*pi*1209*t)+cos(2*pi*697*t); nump=cos(2*pi*1477*t)+cos(2*pi*941*t); t=1000*t; plot(t,num1,t,nump+4,t,4*ones(1,length(t)),'k',t,zeros(1,length(t)),'k') xlabel('time (ms)')

60 We are advocating application-oriented hands-on activities to give students experiences with the actual systems. This helps to understand the concept of what “modeling” is all about. They can begin to see that it’s much easier to use tools like matlab than to try every possibility with the real hardware.

61 The introductory CTSS course at Bucknell has the following formatTwo 14-week semesters per academic year Three 1-hour lectures plus one 3-hour lab session per week Course covers Basic signal modeling System properties Time domain analysis Laplace and Fourier Transforms and Fourier Series Filters and Sampling Discrete transforms and FFT

62 These were the series of labs used in ELEC320 in 2010ELEC Linear Systems and Signal Processing Fall 2010 Lab 1: Introduction to MATLAB Lab 2: MATLAB Exercises Lab 3: Satellite Communications & MATLAB Exercises Lab 4: Tour of Powers Theatre and sound processing demos by Professor Heath Hansum Lab 5: Fourier Series & Data Communications Lab 6: Computation of Fourier Series & Fourier Transforms Lab 7: Analog-to-digital converters, Digital-to-analog converters, Sampling, Nyquist's theorem, Shannon's theorem and Fourier transforms Lab 8: Analog filter design- Lowpass, bandpass, high pass, frequency response, Bode plots, switched-capacitor filters, and Touch-tone. dialing circuits Final Project 62

63 Satellite Communications Project

64 After a certain number of sample delays (in this case about 1After a certain number of sample delays (in this case about 1.675seconds), the output shows the effect of the interference of the reflected signal with ab=0.1. In this case, since the original signal and the reflected signals are both in phase, the output shows constructive interference.

65 Data Communications and Fourier Series ProjectUsing sinusoidal analysis presented in the satellite communication earlier, this project introduces students to Fourier analysis of periodic signals and applications to data communications. In particular, we are interested in determining the harmonic content and the time-response of both the transmitted signal and received signal. We begin with a communication channel with capacity C bits/sec and data is transmitted over a communication channel with bandwidth B Hz. For this project, we consider the transmission of an 8-bit ASCII characters (the control signals are ignored) through our communication channel.

66 Bit rate = 9600 bits/sec. Frequency of 1st harmonic = 9600/8 Hz=1200Hz.The highest harmonic number passed within the bandwidth= This means that the third harmonic is greater than the bandwidth of the filter. shows the original ASCII code at the input of the low-pass filter, the approximation of the signal using three harmonics and a stem plot showing the magnitudes of the first 3 harmonics of the signal.

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68 A simple 3000 Hz bandwidth RC low pass-filter was usedA simple 3000 Hz bandwidth RC low pass-filter was used. The ASCII code for “a” i.e. x(t) is the first plot. The code was programmed in the Agilent 33120A Function Generator and sent to the filter from the LSB to the MSB. The second plot shows the output response of the filter. Since the highest harmonic number passed within the bandwidth is =10, the output of the filter shows a good representation of the input signal.

69 Bit rate = 24,000 bits/sec. Frequency of 1st harmonic = 24000/8 Hz=3000HzSince the highest harmonic number passed within the bandwidth is =1, the output of the filter is not a very good representation of the actual input.

70 Modeling and Control of a DC Motor. Modeling and Control of a DC Motor The purpose of this project was to build, test and characterize a speed control system. The primary objective of this lab was to model systems using differential equationsand Laplace transforms. Students were asked to use Laplace transforms to obtain the open-loop and closed loop transfer functions. The experiment used a DC motor with an AC tachometer . Using rectifiers, the students converted the tachometer signal to DC and using op-amps created a proportional feedback speed control system.

71 Touch-tone® Decoding and FiltersIn this project, we focused on analog filter design for the Touch-tone® telephone dialing system, using the MF10 (universal monolithic dual switched capacitor filter) chip, including a discussion of the history of the development and design issues

72 Fourier Transform

73 Fourier Series Coefficients

74 Fourier Series Coefficients

75 Fourier Series Coefficients

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77 COMPARISON OF COURSE LEARNING GOALS FOR FALL 2008, 2009 AND 2010.2008 2009 2010 Course Learning Goal Mean Median Std. Dev Std. Dev Identify and use signal models 3.1 3 0.99 4.04 4 0.62 4.13 0.92 Develop models of engineering systems, physical systems, and social systems 2.7 2.5 1.16 3.63 0.88 4.2 0.68 Analyze continuous-time system models by applying Fourier and frequency response methods 3.4 3.5 0.97 3.96 0.69 Analyze discrete-time systems 2.9 0.75 3.93 0.96 Develop computer models using available software packages for analysis and design 3.2 0.79 3.75 0.94 4.07 1.1 Design a hardware or software system and formulate system specifications 2.6 2 1.35 3.58 0.83 1.03

78 Three 10-week quarters per academic year The introductory CTSS course at Rose-Hulman, ECE300, has the following format and history Three 10-week quarters per academic year Three 1-hour lectures plus one 3-hour lab session per week Newest version only covers frequency domain. Starts with periodicity and Fourier series Ends with filters and sampling theory Original Version of ECE300 ECE300 is Split Winter New Labs are Introduced Fall

79 The Signals Exploration Platform (SEP) was developed to facilitate a wide variety application-oriented hands-on activities Inputs 1st order To speaker Signal MIC ECG Inst Amp Sampling Impulse Pulse ZOH Bypass Speaker Driver S Up to 6th order To Scope/ Analyzer vy(t) vz(t) clock

80 Nine different labs were developed to cover various topicsWeek Lab Description 1 System linearity and time-invariance in the time domain 2 Intro to spectral measurement (cosine, square, musical instrument via microphone, dual-tone multi-frequency signals) 3 Filtering periodic signals (low duty-cycle pulse train, square, electrocardiogram (ECG), 1st order filter) 4 Harmonic distortion and SNR (distortion of input amplifiers and noise added to signal) 5 Aperiodic signals (speech via microphone) 6 Modulation (cosines, square, sinc, multiplying, speech) 7 Laboratory Practical Exam 8 Filter characteristics (1st vs. 6th order, Chebyshev vs. Butterworth) 9 Real filters and distortion (Chebyshev vs. Butterworth, filtering speech signals) 10 Sampling (impulse, square, and zero-order hold)

81 ? ? Start with very simple exampleEach of the activities that were developed for use with the SEP follows a similar format Start with very simple example Work to a more complicated but textbook-like example Use a real-world example ? ?

82 Lab 3 is about filtering periodic signals and begins with filtering an impulse train with a first order filter. Unfiltered What frequencies are present in the unfiltered signal? How does the spectrum change when you change X in the input signal? Filtered Why are the spectral components below X Hz unaffected by the filter? By what amount is the component at X Hz attenuated? Explain.

83 The next step in lab 3 is to filter a 50% duty cycle square wave.Unfiltered Why is it more difficult to measure the change in each spectral component? Filtered

84 The final step in Lab 3 is that each student gets to measure and filter their own ECG.Unfiltered Which aspects of the ECG signal are affected by the filter and which are unaffected? Explain. Filtered

85 Survey results suggest that students have a much better sense of how the concepts are applicable.Questions with corresponding range of choices and associated values for each end of the range Mean Prior (n=36) Mean during (n=68) p-value 1 I think the concepts that I learned in ECE300 were (1) All theoretical - (5) All application oriented 2.2 2.65 0.0005 2 The labs in ECE300 helped to motivate the material and explain why it is important. (1) strongly agree - (5) strongly disagree 2.58 2.10 0.02 3 Please rate your confidence with using Fourier Series or Fourier Transforms and a system's impulse response to determine the system's output in the time and frequency domain (1) very confident - (4) very unconfident 1.72 2.01 0.04

86 Concept inventory results suggest that how the labs are performed can have a big impact on learning.ECE300 Subset All Questions Avg Class Grade/4.0 Original Version of ECE300 (n=680) Through Fall of 0.42 0.31 2.5 Year Prior to labs (n=25) Winter and Spring 0.38 (p=0.53) 0.28 (p=0.59) 2.75 1st year of labs (n=75) All three quarters of 0.30 (p=0.00) 0.18 2.45 2nd year of labs (n=81) All three quarters of 0.54 0.36 (p=0.13) 2.35

87 Mario has been doing a lot with tablet PCs and interactive examples in lectureCan x(t) be recovered at this sampling frequency?

88 Discussion: How should we design hands-on activities to help students overcome the sources of difficulty?

89 An overview of the technology that we will be working with for the rest of the workshopMario Simoni

90 There are a couple of different technology options to facilitate CT hands-on application oriented activities Signals Exploration Platform

91 The Signals Exploration Platform (SEP) offers several types of inputs and processing paths that can be quickly and easily configured while minimizing debugging Inputs To speaker Signal MIC ECG Inst Amp Sampling Impulse Pulse ZOH Bypass Speaker Driver This was v1(t) S vy(t) vz(t) 1st order To Scope/ Analyzer Up to 6th order YIN Pot -5 to 5 1 ZIN SHORT SAMPLE

92 The power supply is sufficient to drive an 8W load, has less than 5mV ripple noise, and also protects the board. +12 DC input with at least 2A capability (5mm OD x 2.5mm ID adaptor) Reverse polarity protection 1A fuse protection 9V switching supplies with short circuit protection (CUI V R) P-filters to reduce switching noise LED indicators for each rail The fuse can be replaced with a PTC self resetting device

93 The input stage enables you to choose from a variety of signals and then multiply or add to them.Instrumentation Amp INA827 for generic differential to single-ended conversion (gain =10) 9V supply posts provided for Wheatstone bridge applications ECG Input ECG is isolated to 5000V with optoisolator Three ports: ECG_POS (LH), ECG_NEG (RH), and RLD (RL) Requires a separate 9V battery and connector LED indicator for the 9V battery Microphone Input Omnidirectional 100Hz-20kHz electret microphone Gain of 90 and high-pass filter with -3dB at 40 Hz Generic voltage signal input 10k input impedance for function generator and other general voltage signals Multiplier and Adder AD633 handles multiplication and addition of signals Multiplying signal can be selected by switch: 1) time varying input, 2) constant gain between 5, or 3) unity. Adding signal can nulled or set to time varying signal Inputs Signal MIC ECG Inst Amp vx(t) S v1(t) vy(t) vz(t) YIN Pot -5 to 5 1 ZIN

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96 The sampling stage is a loaded switch controlled by a clockThe sampling stage is a loaded switch controlled by a clock. The type of clock and load determine the form of sampling. How to control the sampling switch If the switch is set to SHORT the switch is always closed and the signal passes through unsampled If the switch is set to SAMPLE, then an applied CLK signal will periodically open and close the switch. OPEN switch when CLK = -9V, CLOSED switch when CLK = +9V Low duty-cycle pulses will simulate impulse sampling 50% duty-cycle pulses implements square wave Loading the switch Round fuse holder is for the loading element Load with a 1-5kW resistor for regular sampling Load with a nF capacitor for ZOH type sampling Do not use polarized capacitors CTL IN OUT load

97

98 The filter stage can implement 1st through 6th order filters.OpAmps are pre-wired on board Passive elements go straight across sockets for standard filters Nodes are labeled on the board Stayed with lowpass topologies in order to keep things simple 6th order path has 3 MFB 2nd order stages, can easily bypass a stage 1st Order Path Single Stage of 6th Order Path load load load load Vin load V- Vx Vin load load V- Vout Vout V+ load V+

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100 The output stage can drive both a high and low-impedance load simultaneously with low distortion.V_OUT is before the driver and can only drive high-impedance loads such as oscilloscope SPK_POS and SPK_NEG come from a darlington push-pull output that can drive low-impedance loads The output stage has thermal runaway protection Output voltage saturates at 5V Into an 8W load, the current shouldn’t be greater than 625mA DC The supplies can drive up to 1A in either direction so the load should not be less than 5W or the protection will shut down the board

101 The SEP can be quickly and easily set up and configured to do…Labs In-class demos Homework assignments While minimizing… Debugging time Variability between students

102 In addition to the standard lab equipment, there are several different options for portable lab equipment.

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104 At this point, let’s stop and install the software for the Digilent Equipment on your laptopLocate on the USB drive the following file and click on it Software\digilent.waveforms_v2.4.4.exe

105 Now lets talk about the user interface for the Digilent equipment.

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109 These are the labs that we’ll be working on to familiarize you with the technology

110 Lab 1 focuses on signal modeling and LTI system properties to determine the limitations of the board. Materials 2 function generators and 3-channel scope Mini Lab Steps Questions for students Linearity of amplifiers (Homogeneity) Set the input stage to have a gain of 1. Apply a triangle wave input with a 1V amplitude to the SEP. Double the input amplitude and see if output doubles but doesn’t change shape Continue to increase input amplitude until the output changes shape. Record this amplitude. Change the gain of the input stage on the SEP to 3. Change the amplitude of the input signal until the output just begins to saturate. Compare this amplitude to the value recorded previously How would you describe the boundaries under which the system behaves linearly? How does the gain affect the linearity of the system? Why is it easier to work with linear systems? (Additive) Reset the gain of the board to 1. Apply two equal-amplitude triangle waves with 2x frequency difference to the board such that the board adds them together. Change amplitudes of the two inputs to observe both linear and nonlinear operation. Record the amplitude limitations for which the system behaves linearly. How do the amplitude limitations change when adding signals together? Time Invariance Set the SEP’s gain to be controlled by the potentiometer. Apply a square wave with very short duty-cycle pulses to the signal input. (acts like impulses) Observe that the impulse response is always the same. Set the multiplying signal to by YIN. Set YIN to be a sinusoid (time-varying gain). Observe that the impulse response is now different depending on when it is applied.  Explain how this experiment relates to the definition of time invariance “A delay in the input causes an equal delay in the output, but otherwise the output is unchanged.”

111 Lab 2 focusses on periodic signals with DTMF signals and musical instruments as realistic applications Materials 2 function generators, 3-channel scope, spectrum/frequency analyzer, DTMF generator, musical instrument Mini Lab Steps Questions for students Frequency, amplitude, phase, and power Apply a sinusoid to the primary input of the SEP Measure the output of the board with both a scope and spectrum analyzer Verify that the power and frequency measured on the spectrum analyzer correspond to the scope. Adjust the phase, frequency, and amplitude of the sinusoid and observe how the time and freq measurements change Connect the speaker. Increase the amplitude of the sinusoid until the system no longer behaves linearly. Observe what happens in the time and frequency domains and the sound. Why is the power of the sinusoid not affected by phase or frequency? What happens to the frequency domain measurements and the sound when the system behaves nonlinearly? Sums of sinusoids and periodicity Apply sinusoids to the primary and summing inputs of the SEP and set frequency, amplitude, and phase to be same. Measure the SEP output with the spectrum analyzer and scope and the two inputs with the scope and connect the output to a speaker. Observe what happens to the measurements and sounds as you adjust the phase of one of the sinusoids. Increase the frequency of one of the sinusoids to be 1.1x greater than the other. Change its phase and amplitude. Increase the frequency of one of the sinusoids to be 2x greater than the other. Change its phase and amplitude. Use the DTMF tones of 697Hz and 1209Hz for the number 1. Change the phase and amplitude of one of the signals. Why does phase affect the power level only when the signals have the same frequency? Why does the scope have difficulty capturing the output signal for the DTMF frequencies but the spectrum analyzer does not? Why is the waveform stable on the scope when the frequencies are 2x different but not for the DTMF frequencies?

112 Spectra of other signalsApply a 50% duty-cycle square wave to the primary input of the SEP. Adjust the amplitude, frequency, delay, and duty cycle of the square and measure how the spectrum changes. Increase the amplitude of the square wave so that the system no longer behaves linearly. Measure the spectrum again. Apply a triangle wave to the primary input of the SEP and record the spectrum. Adjust the amplitude, frequency, delay, and symmetry of the triangle wave. Record the spectrum again. Increase the amplitude of the triangle wave until the system no longer behaves nonlinearly. Record the spectrum again. Both the square and triangle waves have multiple frequencies. What is the relationship between these frequencies? Why do the nonlinearities of the system change the spectrum of the triangle wave more than the square wave? Why does the time-delay not affect the power spectrum of the signal? Why does the number of harmonics present change with duty-cycle? Explain this mathematically. Realistic periodic signals Switch to the microphone input on the SEP Connect the scope and the spectrum analyzer to measure the SEP output. Play an instrument into the microphone and record the measurements. (a straw flute or empty water bottle work well, also online keyboard synthesizer ) Determine the fundamental frequency of the signal in both the time and frequency domains. Are they the same? Using a note/frequency chart, determine what note is being played by using the time and frequency domain measurements.

113 Lab 3 introduces filtering and the uses the ECG and DTMF signals as the realistic applicationsMaterials 2 function generators, 3-channel scope, ECG electrodes, DTMF generator, passive parts for filtering Mini Lab Steps Questions for students Using an impulse train to measure the frequency response of a filter Set the input stage to have a gain of 1. Apply a very small duty-cycle square wave to the primary input (behaves like impulse train). Observe the input signal in the time and frequency domain. Measure the power level of the harmonics. Insert passives to make a first-order lowpass filter that has a dB frequency equal to the 4th harmonic of the impulse train. Set the jumpers to filter the signal. Measure the power levels of the first 10 harmonics at the output of the filter, and record the time and frequency plots. Change the passive elements to be a highpass filter. Record the power levels of the first 10 harmonics and the output of the filter in the time domain. What does the output of the filter in the time domain represent? How do the different filters affect the harmonics differently? Using the mathematical model of the filters, estimate how each harmonic of the input signal should change and compare this to the measured values. Filtering Single Sinusoid Reset the gain of the board to 1. Insert passives to make a first-order lowpass filter with a -3dB frequency of 500Hz. Apply a sinusoid to the primary input of the filter with a 1V amplitude and frequency of 50Hz. Sweep the frequency of the sinusoid to 5kHz, taking regular measurements of phase shift and amplitude. Reset the frequency to 50Hz, set the gain and amplitude so that the nonlinearities of the system are very evident. Sweep the frequency of the input signal again over the same range and measure the output in time and frequency. Predict what the output of the filter will be at several different frequencies and verify it with measurements. When the system behaves linearly, what are the only properties of the input that can change? When the system behaves nonlinearly, how does the filter affect each of the harmonics of the signal?

114 Filtering a square waveApply a 50% duty-cycle square wave to the primary input. Insert passives to create a first-order lowpass filter with a -3dB frequency that is approximately equal to the 3rd harmonic of the square wave. Measure the power at each of the first 10 harmonics of the square wave with and without filtering. Record the output of the filter in the time domain. Change the capacitor value of the filter. Then measure the harmonics and record the time domain again. Using the mathematical modeling, predict how each of the harmonics of the square wave will change due to the filter and verify with measurements. Filtering a DTMF signal Set the primary input to be the DTMF signal for the number 3. Insert passives to make a first-order lowpass filter with a dB frequency of 700Hz and a highpass filter with a -3dB frequency of 1400Hz. Record the input signal in both the time and frequency domains. Record the output signals of each filter in both the time and frequency domains. Compare the input recordings to the output recordings. For each of the filters, why is one frequency approximately -6dB below the other frequency? Does the larger amplitude frequency at the output of each filter correspond to the number 3 in the DTMF code? Why are the filters unable to completely eliminate the second tone? Design a continuous-time system that would be able to completely decode the full range of DTMF signals. Looking at an ECG Signal Set up the SEP to measure ECG signals. Insert passives to create a first-order lowpass filter with a -3dB frequency of 100Hz. Record the ECG signal both with and without filtering. Change the -3dB frequency of the filter to be 10Hz. Record the output of the filter again. With the 100Hz filter, at what frequency was most of the “noise” in the signal? Why does the 10Hz filter eliminate most of the noise but not significantly affect the “shape” of the ECG signal?

115 Lab 4 compares the 6th order to 1st order filter and introduces the different types of filters with the real application of filtering a speech signal Materials 2 function generators, 3-channel scope, spectrum/frequency analyzer, passive parts for a 1st order lowpass filter and 6th order Butterworth, Chebychev, and Bessel lowpass filters. Mini Lab Steps Questions for students For each of the types of filters, perform the following steps Apply a very low duty cycle pulse wave to the input signal and adjust the scope to capture just a single impulse response of the filter. Use the spectrum analyzer to display the power spectrum of the impulse response. Change the input signal to be a sinusoid with 1V amplitude Plot the input and output signals on the scope and measure the change in amplitude and phase as you sweep the frequency of the input signal Why is the power spectrum of the impulse response similar to the plot of the gain that you measured from the sinusoids at different frequencies? Explain why the phase shift jumps from negative to positive between adjacent frequency steps for the 6th order filter. Why doesn’t it jump like this for the first order filter? Filtering a speech signal Apply the “these” waveform to the input signal Using each of the three filter pathways in turn: unfiltered, 1st order, and 6th order, listen to the output of the filter on the speaker. Working with a partner, switch to the microphone input and have one partner speak into the microphone while the other listens to the speaker Why do the 1st order and 6th order filters make the speech sound different even though they have the same cutoff frequency? What sounds from the word “these” are eliminated by the filters and which remain? Explain. When speaking into the microphone, which consonant and vowel sounds pass through the filter mostly unaltered? Explain.

116 FilterPro from Texas Instruments is an excellent piece of software for designing op-amp based filters.

117 Here is the circuit schematic for the filters and the table that is used to collect data.1st order filter Name Value R1 (Stage 1) 6.2K R2 (Stage 1) C1 (Stage 1) 100nF 3 stage cascade of 2nd order MFB circuits for 6th order Chebychev Type I lowpass filter with fc=250Hz and 2dB of ripple in the stopband.

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119 This is what the unfiltered speech signal should look like for the word “these”.

120 Lab 5 introduces sampling and filtering to recover a sampled signal with speech as the realistic example Materials 2 function generators, 2-channel scope, and passive for a 1st order and 3rd order filter, a 1kW resistor and 10nF capacitor for sampling Mini Lab Steps Questions for students Sample and recover a COS4 waveform using impulse sampling Install a 1kW resistor into the sampling -switch load socket Apply a 100ms pulse signal at 1kHz to the CLK input Apply the COS4 signal to the input signal at 50Hz Observe the input and output signals on the scope in both time and frequency for the following conditions: Unfiltered 1st order filter 6th order filter Repeat the experiment with sampling frequencies of 500Hz and then 200Hz Why does the 1st order filter create a better recovered signal for the ZOH sampling than the other forms of sampling? Explain how aliasing can occur even if the sampling frequency is higher than the Nyquist rate. Explain why the 6th order filter does a better job of recovering the signal than the 1st order filter. Explain how and why the copies of the original spectrum are different for the three different forms of sampling. Explain why you can recover the signal with a lower order filter when using ZOH sampling. Sample and recover a COS4 waveform using square wave sampling Repeat the same series of experiments but change the CLK signal to be a 50% duty cycle square wave. Sample and recover a COS4 waveform using ZOH sampling Replace the 1kW resistor in the sampling -switch load socket with the 10nF capacitor. Repeat the same series of experiments but change the CLK signal back to the 100ms pulse at 1kHz. Sampling a speech signal Go back to the setup for the impulse sampling, but change the input signal from COS4 to “these” Design a first order filter to recover the speech signal. Starting at 500Hz, increase the sampling frequency until the word sounds normal. Explain why the sampling frequency had to be increased in order for the word to sound normal. Explain the relationship of the necessary sampling frequency to the spectrum of the word “These”

121 Now it’s up to you to develop an activity using this technology that is grounded in our original discussion of learning difficulties

122 Where do we go from here?

123 We are still working out how to make the boards available to everyoneWe are still working out how to make the boards available to everyone. You can build your own by following these steps… Find a PCB manufacturer Silver Circuits (www.custompcb.com) $8/board for 30 boards Advanced Circuits (www.4pcb.com) Send them the following files for production TOP.art BOTTOM.art SST.art SMT.art SMB.art ece300_board_ drl Order parts ECE300_BOARD_2013_BOM.xlsx has all of the components from Digikey Also need 12V DC power supply with greater than 3A. Nothing special, can get anywhere. Assemble the boards Surface mount and through-hole parts Reasonable for experienced technician to build 10 in one week while doing other things.

124 There are many possible ways to continue this discussion and collaborate further…Gather similar historical data at your schools Publishing new activities that we develop and test together Eventually develop and submit a Type II TUES proposal together Order PCBs together to reduce cost