Session F1G

978-1-61284-469-5/11/$26.00 ©2011 IEEE October 12 - 15, 2011, Rapid City, SD

41st ASEE/IEEE Frontiers in Education Conference

F1G-1

Wow! Linear Systems and Signal Processing is fun!

Maurice F. Aburdene and Kundan Nepal Electrical Engineering Department, Bucknell University, Lewisburg, PA 17837

Abstract - We describe a recent offering of a linear

systems and signal processing course for third-year

electrical and computer engineering students. This

course is a pre-requisite for our first digital signal

processing course. Students have traditionally viewed

linear systems courses as mathematical and extremely

difficult. Without compromising the rigor of the

required concepts, we strived to make the course fun,

with application-based hands-on laboratory projects.

These projects can be modified easily to meet specific

instructors’ preferences.

Index Terms- Linear Systems, Signal Processing, Signal

Processing Education, Student Learning

INTRODUCTION

Most undergraduate programs in electrical and computer

engineering require a course in linear systems, signals and

systems, signal processing, or a similarly named course in

the third year. There are many excellent texts in these areas

(too many to list here). The texts and courses “focus” on

continuous-time signal representation, discrete-time signal

representation, sinusoidal signal analysis and design

methods, linear system definitions and methods,

differential equations, difference equations, modeling of

systems, spectral analysis, Laplace transforms, analog

filters, sampling, Z-transforms, digital filters, continuous-

time Fourier series, convolution, and continuous-time and

discrete Fourier transforms. In addition, many texts and/or

linear systems classes incorporate software, such as

MATLAB®, Spice, Mathematica®, Mathcad® or locally

developed software. We have tried to teach all of these

topics in our classes and as instructors, we think they are

great and try to impart our excitement to our students.

Pendergrass states that students have difficulty in such

courses since they view them as “only math and theory” [1].

Greenberg, Smith and Newman found that many students

had “difficulty mastering the fundamentals of spectral

analysis, appearing to be overwhelmed by the interaction of

multiple variables” [2].

In addition, if you teach one of the linear systems courses,

then you might have observed that such a course is

perceived by students as:

Theoretical and mathematical[1],[2]

Notation intensive[2]

Difficult [1]-[4]

Fast paced and time-intensive

Counterintuitive, when moving from continuous-

time domain to discrete-time domain

Educators have tried to address the above concerns. For

example, Ferre, Giremus and Grivel have tried to make the

course more appealing by focusing on small-group based

learning projects [5]. Wright, Morrow, Allie and Welch

suggested ways to enhance engineering education and

outreach [6], and Turner and Hoffbeck suggested ways to

put theory into practice using software [7]. Warren

suggested using computational projects to optimize student

learning and retention of fundamental concepts [3]. Buck

and Wage proposed active and cooperative learning (ACL)

in signal processing courses [4].

In the summer of 2009, we decided to tackle the issue and

completely redesign the course, ELEC 320 (Linear Systems

and Signal Processing), trying to make it as much a fun

course for the students as it is for the instructors. The basic

idea was to make the course application-based and to have

hands-on laboratory projects. Our goal was to have students

view the course as an opportunity to learn most of the above

topics (very ambitious goal) and have fun. We decided not

to choose a new text, but rather, use the texts that students

had used earlier, along with web based-resources, and

industrial application notes [8]-[11]. We taught the course in

the fall of 2009 using seven projects (applications) in

addition to an introduction to MATLAB and a final project.

Each application and the major concepts involved were

discussed first in class. Students were asked to perform

experiments in lab to improve their understanding of the

major concepts and their applications. Students were then

required to write project reports (learn by writing). The

course also required the students to propose a final project

that covered one or more areas learned in the classroom.

The students then devote the final three weeks of the

semester designing and implementing their ideas to produce

a functional product. Two of the projects are described in

detail in [12].

PROJECTS AND APPLICATIONS

I. Introduction to MATLAB Using Circuit Examples

Throughout the semester, students used MATLAB to

analyze linear systems and signals applications and

problems. Our students have had prior programming

experience using JAVA and we used two introductory labs

to focus on helping students familiarize themselves with the

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41st ASEE/IEEE Frontiers in Education Conference

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MATLAB interface and learn its rules and syntax. The labs

focused on the representation of signals as arrays and

matrices; processing of these arrays and matrices; plotting of

signals and conditional statements and loops. In order to

show how MATLAB might be used to analyze signals, two

examples were chosen. In the first example, students were

asked to analyze an inverting op-amp circuit; create both a

DC and AC input signal and analyze the output response in

each case. For the second example, students were asked to

create a signal by combining three sinusoidal waveforms to

approximate a square wave signal with 1 kHz frequency.

Students were then tasked with using this signal as an input

to a series RC circuit with bandwidth of 1.5 kHz and to

derive and plot the output voltage across the capacitor.

These examples were an indirect introduction to the Fourier

series and analog filters incorporated in some of the course

projects.

II. Satellite Communications

FIGURE 1

A SIMULINK MODEL OF A SATELLITE COMMUNICATIONS

SYSTEM.

Communication systems provided us with excellent

applications of important concepts that students had studied

in ELEC 120 (Foundations of Electrical Engineering) and

ELEC 225-226 (Circuit Theory I &II). This project

introduced students to a satellite communication system

where a signal is transmitted from a ground transmitter,

received by the satellite after some delay and reflected back

to the ground receiver [12]-[14]. Students analyzed the

signal received by the ground station as the sum of the

signal sent from the station and the signal reflected back

from the satellite. This interesting project helped students

review sinusoidal signals, phasors, power, and understand

the effect of delays, echoes and fading. In addition, the

students got an opportunity to learn more about MATLAB

and Simulink while getting to implement fundamental

concepts they had previously learned as shown in Figure 1.

This project is fully described in [12].

III. Data Communications and Fourier Series

In this project, we focused on Fourier analysis of periodic

signals and applications to data communication [12]-[15].

Students were given the task of analyzing an 8-bit ASCII

character transmitted at a particular bit rate over a

communication link with a given bandwidth. In particular,

we were interested in having the students determine the

harmonic content and the time-response of both the

transmitted signal and received signal. Students

programmed the Agilent 33220A 20 MHz Function

Generator to create the ASCII character and created a filter

to view and analyze the output response. Students also used

MATLAB and Simulink to simulate the communication

model. This project reinforced concepts of periodic signals,

Fourier series, harmonics, phase shift, signal power, bit rate,

link bandwidth, Nyquist's theorem and Shannon‟s theorem

for data transmission on a noisy channel. Details of this

project are presented in [12].

IV. Modeling and Control of a DC Motor

FIGURE 2

TOP VIEW OF BOARD WITH DC MOTOR AND SENSORS.

The purpose of this project was to build, test and

characterize a speed control system [16]. The primary

objective of this lab was to model systems using differential

equations and Laplace transforms. Students were given a

differential equation model of a DC motor and 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 as shown in Figure 2. Using

rectifiers, the students converted the tachometer signal to

DC and using op-amps created a proportional feedback

speed control system.

AC

TachRectifier

Amplifier

M

DC Motor

+-

Vref Out

FIGURE 3

MODEL OF THE SPEED CONTROL SYSTEM.

For this project, students were asked to build the system

shown in Figure 3 and answer the following questions:

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41st ASEE/IEEE Frontiers in Education Conference

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Let va be the input voltage to the motor, τ=6.7 sec and K=

46 rad/sec-volt. The motor speed, the output, can be

determined directly from the equation written as:

What is the step response of the system?

What is the transfer function H(s) = W(s)/Val(s) based

on this equation?

Draw a block diagram of the closed-loop (CL) control

system. Obtain the transfer function of the CL system.

Use a square wave as your input voltage and observe

the speed of the motor and the rectifier output voltage

using the oscilloscope. What is the time constant of the

closed loop system? Can you determine K and τ?

V. Touch-tone® Decoding and Filters

FIGURE 4

PROGRAMMABLE FILTER BOARD.

In this project, we focused on analog filter design for the

Touch-tone® telephone dialing system [17], using the MF10

(universal monolithic dual switched capacitor filter) chip,

including a discussion of the history of the development and

design issues. To minimize the time devoted to building the

detection filters, a circuit board with an MF10 filter (shown

in Figure 4) was given to the students. The circuit board had

the necessary clock generator, audio jacks, operational

amplifiers and an area to wire circuit components. Students

were tasked with using the MF10 datasheet to create the

required filter to detect a particular touch-tone. Based on

their calculations, students then programmed the board by

proper selection of resistors. Here is a sampling of some

questions from this project:

In your own words describe the Touch-tone® telephone

dialing system. How many tones are generated per

pushbutton? What are the frequency assignments for

the pushbuttons?

Suppose the transmitter was nonlinear, list the first

three harmonics of each frequency. Compare these

harmonics with the original frequencies.

Develop a block diagram(s) for a detection system

using analog filters.

Design a lowpass/highpass filter with a 1 kHz

bandwidth. Test your design using a tone generator

program (Dual-Tone Multi-Frequency, DTMF) and the

sound card. Observe and record the output of the filter

when you push the 1 button. Observe and record the

output of the filter when you push the # button.

Using the output of the filter as an input, design a

bandpass filter to detect the 7 button. Compare the

output of the filter with output when depressing other

buttons. What is the frequency response of the filter?

What would happen to your detector circuit if the

transmitter frequencies varied by ±2%?

VI. Analog-to-Digital and Digital-to-Analog Converters

The objective of this project was to help reinforce the

concepts of analog-to-digital converters (A/Ds), digital-to-

analog converters (D/As), sampling and digital signal

processing. Students used the Keithley KUSB-3100 data

acquisition hardware, the sound card and MATLAB for

signal acquisition and processing. Students created

waveforms using a function generator, sampled the

waveforms at various sampling rates using the KUSB

hardware and then processed the samples using MATLAB

to generate the magnitude and phase plots using fast Fourier

transforms (FFT). Students also sampled and recorded

sound at various sampling rates using the sound-card and

processed it using MATLAB/Simulink. Here is a sampling

of some questions from this project:

Please study the Keithley KUSB 3100 data sheet and

answer the following questions: How many bits does

this A/D have? What is the maximum analog input

voltage? Develop the digital output vs. analog input

characteristic? What is the maximum, minimum and

average conversion error? Assume that the conversion

error introduces noise, what is the signal-to-noise ratio

for a 12-bit A/D?

In your own words, describe (a) Nyquist‟s sampling

theorem and (b) Shannon‟s theorem for noisy channels.

Using the MATLAB program provided, sample a 200

Hz sinusoidal 1V peak-to-peak signal. Now modify the

program to sample (a) two periods of the input signal,

(b) the input signal at 50 Hz, 200Hz, 500Hz, and 1 kHz.

Relate the above to the Nyquist sampling frequency.

Use the MATLAB fft program to determine magnitude

and phase spectrum of the input signal. Repeat this for a

square wave signal.

Use the program to sample a sinusoidal input signal

using the A/D and to output the sampled signal using

the D/A. Observe the input and output on the

oscilloscope.

Just like the Keithley board, the sound card in your

computer can be used to acquire analog signals.

Assume the sampling frequency is 8 kHz and a signal is

sampled for 10 seconds. How many samples are

collected? What is the time difference between two

samples?

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41st ASEE/IEEE Frontiers in Education Conference

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Set up your function generator to generate a sinusoidal

signal of 2 kHz. Connect a speaker to the function

generator. Now set the sampling frequency of your

program to 8 kHz and acquire 2 seconds of data. Plot

the data just acquired and play it using the sound

command in MATLAB.

Now change the function generator frequency to 6 kHz.

Acquire 2 seconds of data and view the data using the

plot command. Does the data look the same as before?

Play the sound using the sound command. Does it

sound the same? Repeat this for a sampling frequency

of 11,025Hz.

Instead of some tone generated through the function

generator, let us actually work on real speech signals.

Using the MATLAB program, record a voice at a

sampling frequency of 22,050 Hz. Play it using the

sound command. Now change the sampling frequency

to 11,025 Hz. Play it using the sound command again.

Do you hear any difference?

VII. Digital Filter Design

This project used the previous project on A/D, D/A and

sampling as a foundation to introduce students to Finite

Impulse Response (FIR) and Infinite Impulse Response

(IIR) filters. Students used MATLAB/Simulink to describe

the difference equations and interpret the transfer function

of the filters and perform an analysis of the frequency

response of the filters. In addition, students tested the

different filters by using their favorite music as inputs to the

filter. Here is a sampling of questions from this project:

In your own words, describe FIR and IIR filters. What

are the advantages/ disadvantages of both the IIR and

FIR filters?

Let x[n] = ∂[n]. Find y[n] = x(n-N). Let N=4. Sketch

y[n] vs. n. Find H(z) =Y(z)/ X(z). Sketch the amplitude

of H(z) vs. ω and phase of H(z) vs. ω. Discuss your

results.

Let x[n] = ∂[n]. Find y[n] = (x[n] + x[n-1] + ... + x[n-

(N-1)/N]) with N=4. Sketch y[n] vs. n. Find H(z) =Y(z)/

X(z). Sketch the amplitude of H(z) vs. ω and phase of

H(z) vs. ω. Discuss your results.

Load your favorite music file into MATLAB, x[n].

Implement the filter and listen to the filtered output

using the sound card. Experiment with various values of

N. Discuss your results.

Assume zero initial conditions. Let x[n]= ∂[n]. Find

y[n] = -αy[n-1] +x[n-1]. Sketch y[n] vs. n. Find H(z) =

Y(z)/X(z). Sketch the amplitude of H(z) vs. ω and phase

of H(z) vs. ω. Discuss your results. Implement this filter

and listen to the filtered output of your music file.

Experiment with various values of α. Discuss your

results.

Now implement the filter y[n] = x[n] - x[n-1]. Listen to

the filtered output of your music and discuss your

results.

VIII. Convolution: Computations and Applications

This project was designed to help students learn about the

impulse response of continuous-time systems and see the

practical application of convolution. Students were first

asked to determine the impulse response of an RC circuit

both analytically and experimentally. Then they were asked

to use convolution to determine the response to various

input signals. In addition, the class went to measure the

impulse response of the Powers Theatre (on campus). As an

application of convolution, students were asked to

experiment with music by taking their favorite music and

using convolution to determine how the music would sound

in the theatre. The trip to the Powers Theatre also

demonstrated some of the basic concepts discussed in the

satellite communications project. Here is a sampling of

some questions from this project:

Consider a series RC circuit driven by a voltage source,

with the output voltage measured across the capacitor.

We will use R = 10 kΩ and C = 0.1 μF. Analyze this

circuit and derive the expression for the impulse

response, h(t). In your analysis, consider applying a

rectangular pulse that gets briefer and briefer while

maintaining unit area.

Analyze the circuit and derive an expression for the

output, y(t).

Devise a procedure to experimentally measure the step

response of the circuit.

Obtain the impulse response of the circuit, h(t).

Use convolution to predict the response of this circuit to

a 5 volt step function. Apply a 5 volt square wave and

compare the response with your prediction.

Use convolution to predict the response of this circuit to

a 2 volt sinusoidal signal, f(t) = 2 sin(ωt). Then apply a

2 volt sinusoidal signal and compare the response with

your prediction.

Using the Keithley USB board, sample the impulse

response, h(n), of the RC circuit.

Load a music file, x(n) and convolve it with h(n) using

the conv function. What effect does convolution with

h(n) have on the music, i.e. what is different about the

music after the processing?

Load the impulse response of the Powers Theatre. The

objective is to use convolution to hear digitized music

and then play the resulting music and to listen to it as if

you are in the Powers Theater. Plot the impulse

response, h(n), of the Powers Theater vs. sample

number.

Load a music file, x(n) and convolve it with h(n). Play

x(n) and y(n). What effect does convolution with h(n)

have on the music?

IX. Final Projects

Students were asked to propose their own project that

covered one or more concepts learned in the course. The

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41st ASEE/IEEE Frontiers in Education Conference

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final project, which spanned three weeks, involved the

design, implementation, test and documentation of a

complete system (either hardware or software). At the end

of the semester, students were required to demonstrate a

working system to the class and guests, and prepare a

professional presentation. In addition, students were

required to write a technical report that documented their

design, a product specification datasheet for use by the

marketing group, and a sales brochure. The open-ended

nature of the project yielded a number of interesting

projects.

ASSESMENT

Since the course underwent a major redesign, and we had

tried a new project based approach to the course, it was

important for us to find out how the students perceived the

different projects. At the end of the semester (Fall 2009),

students were asked to fill out an anonymous survey which

included that they indicate “what labs you found helpful so

we can improve them.” The result of the survey is presented

in Figure 5 for each project. A total of 24 students

responded to the survey and rated each project on a scale of

1 to 5. A rating of 1 indicates that the students did not find

the project helpful while a rating of 5 indicates the students

found the projects very helpful in enhancing their

understanding of the concepts involved. Students

overwhelmingly seemed to like the first project titled

“Introduction to MATLAB using Circuit Examples”. The

final project received high scores as well. This is not

surprising since the students had themselves worked to

create the project specification, planned it, and implemented

the project. The median for each project was 4 out of 5,

indicating general satisfaction with the projects in helping

the students understand the concepts involved.

FIGURE 5

RESULTS OF THE END-OF-SEMESTER STUDENT SURVEY FOR EACH PROJECT (TOTAL RESPONDENTS= 24 STUDENTS).

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978-1-61284-469-5/11/$26.00 ©2011 IEEE October 12 - 15, 2011, Rapid City, SD

41st ASEE/IEEE Frontiers in Education Conference

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TABLE I

COMPARISON OF COURSE LEARNING GOALS FOR FALL 2008, 2009 AND 2010.

2008

2009

2010

Course Learning Goal Mean Median

Std.

Dev Mean Median

Std.

Dev Mean Median

Std.

Dev

Identify and use signal models 3.1 3 0.99 4.04 4 0.62 4.13 4 0.92

Develop models of engineering systems,

physical systems, and social systems 2.7 2.5 1.16 3.63 4 0.88 4.2 4 0.68

Analyze continuous-time system models

by applying Fourier and frequency response methods 3.4 3.5 0.97 3.96 4 0.69 4.13 4 0.92

Analyze discrete-time systems 2.9 3 0.88 3.96 4 0.75 3.93 4 0.96

Develop computer models using available software packages for analysis and design 3.2 3 0.79 3.75 4 0.94 4.07 4 1.1

Design a hardware or software system and

formulate system specifications 2.6 2 1.35 3.58 4 0.83 3.93 4 1.03

Table I shows a comparison of the course learning goals for

the course offerings in 2008, 2009 and 2010 using the same

scale as the survey. The classes had 10, 24, and 15 students

respectively. The course offered in 2008 was a traditional

text [14]/lecture/lab format and did not use the projects

discussed in this paper. Students responses show that scores

for the course learning goals improved from 2008 to 2009 as

a result of the move to a project based course. The learning

goals results for 2010 shows further improvements in all but

“analyze discrete-time systems.”

SUMMARY

This paper presented an overview of our project based

course on linear systems and signal processing. As

instructors, our motivation was to dispel the notion that this

type of course is too mathematical and difficult to be fun

and exciting. Through application oriented projects, we tried

to convey the enthusiasm we have for the subject to our

students in the course. An end of semester survey (Fall

2009) showed that while students did in fact enjoy the

project driven approach, we have room for improvement.

Based on the survey and our own analysis, the course was

modified from this offering in the fall of 2010. We dropped

the modeling and control of a DC motor and have gone back

to requiring a textbook [14] for the course. Textbooks from

previous classes that we thought would have been kept by

students as “reference” materials for their own private

“libraries” were, in fact, sold back.

ACKNOWLEDGEMENTS

We thank Professors Rich Kozick, Heath Hansum, James

Baish, and Mr. Tom Thul for their valuable help with the

design of the projects.

REFERENCES

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[3] S. Warren, “Optimizing Student Learning and retention of time and frequency domain concepts through numerical computation projects,”

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[11] Agilent Technologies, “The Fundamentals of Signal Analysis”, Application Note 243.

[12] M. F. Aburdene, and K. Nepal, “Satellite Communications, Data

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[13] D. R. Fannin, W. H. Tranter, and R. E. Ziemer, “Signals and Systems:

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[15] A. S. Tanenbaum, “Computer Networks (3rd Edition),” Prentice-Hall, 1996, (Chapter 2, pp. 78-81).

[16] R. C. Dorf, and R. H. Bishop, “Modern Control Systems (11th Edition),” Prentice-Hall, 2008.

[17] L. Schenker, "Pushbutton Calling with a Two-Group Voice

Frequency Code," The Bell System Technical Journal, vol. 39, pp.335-255, January 1960.