This page last updated Wed. July 31, 2013

ELEC 2120 Linear Signals and Systems

Summer 2013 Dr. Roppel

Welcome to Linear Signals and Systems.  Please feel free to offer suggestions for improving the course and this course web site. If you find a link that might be of interest to the class, email the URL to me and I might include it on this page. Please note that this web page is archival, and is not a substitute for attending class. Announcements and assignments that are made in class might not appear here for several days.

ANNOUNCEMENTS

o   First class meeting is Friday, May 17 at 11:30 – 12:45 in BROUN 235 (note room change).

o   Virtual class on Wed. June 19. No class meeting. Notes & activities will be posted.

o   No class meeting on Fri. June 21 per AU calendar.

o   Virtual class on Fri. July 5. No class meeting – notes and activities will be posted.

 

CLASS PROCEDURES (Changed test dates may not be reflected on the syllabus or daily planner. See the Announcements section above for changes.)
Syllabus 
Daily Planner    Revised July 2

Homework Preparation  html

              Homework Examples  ex. 1    ex. 2    ex. 3

TEXTBOOK
Kamen and Heck, Signals and Systems, 3nd Edition, Pearson Prentice-Hall, 2007.  Authors' textbook link

TESTS

Test 1 is Wed. June 12.  Study guide.  Solution

Test 2 is Wed. July 10.   Study guide  Solution

Final Exam is Tues. July 30, noon – 2:30.  Study guide:  docx   html   solution

 

NOTES FROM THIS SEMESTER

Lecture Date

Item Description

5/17/2013

Chapter 1 slides

5/22/13

Chapter 2 slides – part 1

5/24/13

Chapter 2 Sect. 2.2, 2.6 convolution

5/29/13

Chapt. 3 Sect. 3.1-3.2 Fourier series trig. form

5/31/13

Chapt. 3 Sect 3.3 Fourier series complex exponential form

Updated 6/3 with corrections on page 4 (in red) related to the phase spectrum.

6/3/13

Chapt. 3 Sect 3.4-5  Fourier transform – some notes added after lecture in red on pp. 5, 7

6/5/13

Chapt. 3 Sect. 3.6-7 Fourier transform properties

6/7/13

Chapt. 3, Sect. 3.7-8 Modulation and F. transform of periodic sig.’s

-updated after class with slight correction to DSB equation.

6/10/13

Discussed some of the textbook worked problems and worked In-Class 9.

6/17/13

Ch. 4, Sect. 4.1-4.2. Finished DTFT and introduced DFT / FFT

6/24/13

DFT example and Ch. 5, Sect. 5.1-2  Cont. time systems and filters

6/26/13

Sections 5.3, 5.4 – Filters, sampling, and reconstruction

6/28/13

Laplace – part 1 w/ in-class 15

7/1/13

Laplace – part 2 w/ in-class 16

7/3/13

Laplace – Transfer Functions and Block Diagrams – 6.5, 6.6

7/8/13

Laplace – Lowpass Feedback Amplifer

7/17/13 wed.

Chapt. 8 – stability, step response for 1st-order systems

7/19/13 fri

Chapt. 8 – step response of 2nd order sys., and intro to 8.4 Bode plots  pdf

7/22 mon.

Chapt. 8 – Bode magnitude plots

7/24 wed

Chapt. 8 – filter types and frequency transformations  pdf

7/26 fri

Chapt. 8 – phase plots    Example test question

 

 

HOMEWORK & SOLUTIONS

Cover sheet /
complete assignment

Assigned

Due

Comments / Description

HW 1

Fri 5/17

Wed 5/22

Prob.’s from Chapt. 1. Prob. 11 only for submission.

Prob. 11 plot corrected on Sat. 5/18.

Solutions

 
HW 2

Fri. 5/24

Wed. 5/29

Prob.’s from Chapt. 2. One problem only (Prob. 2) is to be submitted on Canvas. Paper submissions will not be accepted.

Solution 

Debriefing – includes common errors, as well as clever approaches from students.

 
HW 3

Fri. 5/31

Wed. 6/5

Prob.’s from Chapt. 3. Complex exponentials and Fourier series.

Submit Prob. 2 ONLY on Canvas.

Some of my results: c(1) = -0.318, c(9) = 0.0707

Solution – thanks to Andrew Cookston

 
HW 4

Wed. 6/5

Mon. 6/10

Prob.’s from Chapt. 3 – Fourier transforms & modulation. Submit only Prob. 2. Submit on paper (not Canvas).

Solution – thanks to Audrey Rose Shapland. (Updated 6/18 with slight correction.)

 
HW 5

Mon.7/1

Mon. 7/8

Submit on Canvas:  Prob. 1: Mystery signal DFT

HW 5 mystery signal (.wav file)   Solution.

 

Not for submission:  Chapt. 6 Worked Prob.’s – Laplace Transforms

 
HW 6

Mon. 7/22

Fri. 7/26

Submit on Canvas.  Filter design

Solution guide  updated Wed. 7/24.   docx   pdf  

 

 

IN-CLASS WORKSHEETS and SOLUTIONS

No.

Date

Comments / Description

1

Fri. 5/17

Chapt. 1 – part 1

Solution – thanks to Carroll Aby

2

Mon. 5/20

Chapt. 1 – part 2 (Submit in class on Wed. 5/22)

Solution – thanks to Micah Hayes

3

Wed. 5/22

Chapt. 2 – part 1

Solution – thanks to Andrew Cookston

4

Fri. 5/24

Chapt. 2 – part 2 convolution

Solution – thanks to Jake Austin

5

Wed. 5/29

Example 3.2 – calculate harmonic amplitudes and plot amplitude spectrum.

Assignment is on last page of notes for 5/29. Solution – thanks to Alex Sylvis.

6

Fri. 5/31

Calculate complex expon. form of Fourier series for given waveform. (Waveform from Chapt. 3 worked problems in textbook.)

Solution – thanks to Walter Conway    Detailed solution from textbook website.

7

Mon. 6/3

Calculate the Fourier transform of a pulse waveform. (Waveform from Chapt. 3 worked prob.’s – F. transform, #1).

Solution – thanks to Nicholas Allen-McCormack.

8

Wed. 6/5

Calculate the DBSC modulation of a cosine.

Solution – thanks to Chris Hathcock.

9

Fri. 6/7

Fourier transform of a periodic signal (pulse train)  Worksheet 

(Note: We did not do this in class due to a fire alarm. Try it on your own and we will discuss in class Monday.)

Solution – thanks to Paul Copeland.

10

Fri. 6/14

Fourier transform of a modulated sinc function.

Solution – thanks to Sam Roberts.

11

Mon. 6/17

Evaluation of Eq. 4.22 for k = 0 using Taylor series approx.

Solution (coming soon)

12

Wed. 6/19

Questions from Sect. 4.2 and 4.3 on the DTFT and DFT.  Word   PDF  (Updated Wed. 6/19 to correct the title from I-11 to I-12.)

For the virtual class meeting, read Sect. 4.2 & 4.3, complete this worksheet, and bring it to the next class meeting on Mon. 6/24.

Solution – thanks to Jared Bredin.

13

Mon. 6/24

Ideal filters.  Solution – thanks to Hannah Masten

14

Wed. 6/26

Sampling and reconstruction  Solution

15

Fri. 6/28

RC circuit – step response and sinusoidal steady state response.

See in-class 16 for solution.

16

Mon. 7/1

Rework of in-class 15.Solution

17

Wed. 7/3

Transfer function of a feedback system. Solution

18

Mon. 7/8

Lowpass feedback amplifier calculations  Solution – thanks to Shane Williams

19

Fri. 7/12

DFT, sampling theorem, f = k(SR/N), ideal LP and HP filters  Solution

20

Mon. 7/15

8.1 – 8.3. Stability, 1st & 2nd order step response. Solution

21

Wed. 7/17

First order step response.  Worksheet  (submit Fri. 7/19)  solutions

22

Mon. 7/22

Write TF from Bode mag. plot. Solution - thanks to Calvin Wagner

23

Wed. 7/24

Convert low-pass to high-pass  Solution

 

MY CODE
Code used for class demos and homework.

 

Code

description

1

sum_of_harmonics.m

Sums harmonics to generate a square wave. User chooses number of harmonics.

2

Imagefft.m

Several artificial images are used to demo applying the 2D fft to images.

3

ex43_dtft_pulse.m

dtft_pulse.m

Plot of DTFT of a pulse from Example 4.3 (su 2012)

2013 version of same.

4

trunc_sinc.m

Recover a continuous-time pulse after bandlimiting its transform.

5

pulse_fft.m

Recover a discrete-time pulse after bandlimiting its discrete Fourier transform.

6

dft_count.m

Examine the relationship f = k(SR/N) where f = freq. in Hz, k = DFT index, SR = sampling rate, and N = record length.

7

lowpassfilter.m

Digital LPF implemented by time-domain convolution (Sections 5.5-6).

8

butterworth.m

Design of a Butterworth LPF following Sect. 8.6.1

9

bandstop.m

Design of a Butterworth bandstop filter based on the LPF prototype.

10

plot_sinc.m

ezplot of symbolic sinc

11

ft_pulse.m

ezplot of Fourier transform of a single pulse.

 

ADDITIONAL NOTES FROM PREVIOUS SEMESTERS

Date Posted

Item Description

7/23/12 Mon

Butterworth filters pdf

7/20/12 Fri

Sinusoidal steady response of a 2nd order system  pdf

7/18/12

Step response of a 2nd order system  pdf

7/16/12

Laplace, Bode, and all those damped sinusoids (contains in-class #14)...  pdf

7/6/12

A Digital Low-Pass Filter  docx  pdf   (contains in-class #12)

6/29/12

“A Filter for Every Occasion”   docx   pdf

6/27/2012

“Looking Through the (Sampling) Window” lecture from Wed. 6/27/12  docx  pdf

6/20/12

“Bandlimiting a Pulse” lecture from Wed. 6/20/12   docx   pdf

6/18/2012

“Sinc or Swim” lecture notes from Friday 6/15/12  docx  pdf

6/13/2012

Image processing using 2D fft    Theory page    Example page (JAVA)

5/16/2012

Fourier and Laplace transform tables from text – use these for reference on tests, HW, etc.

6/1/2011

recur.m and other MATLAB stuff on the Mathworks website

4/23/08

Step response of a 2nd-order underdamped system - notes

4/9/08

Water pump spectrum analyzer - just because they could...Ga. Tech  (thanks to Stephan Henning)
http://www.hackaday.com/2008/04/07/h2o-spectrum-analyser/
 

3/10/08

Inferring signal amplitudes from FFT results - technical paper

2/11/08

Page with nice java-based demos  http://www.jhu.edu/signals/

1/28/08

Link to "The Scientist and Engineer's Guide to Digital Signal Processing" By Steven W. Smith, Ph.D.
---see Chapt. 6 for a good discussion of discrete convolution  (click here for local copy of Chapt. 6).

1/28/08

Demo:  Sum of sinusoids demo (integer freq. ratio --> periodic sum, textbook Sect. 1.1.3)  sumsins.m   sumsnd.m

1/23/08

MATLAB discrete solution to 1st-order diff. eq. for an RC circuit,  as shown in Eqn. 2.61

1/11/08

Jeff Hawkins - "On Intelligence"  (NPR radio interview)  - posted 7/23.07  website  mp3

1/11/08

Tartini music analysis software:  http://miracle.otago.ac.nz/postgrads/tartini/
"A Smarter Way to Find Pitch" - discussion of the Tartini software

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SOFTWARE SUPPORT

MATLAB: There is no free portable version of MATLAB. The full version is installed on the COE workstations. The bookstore sells the student version for about $100. There are help and tutorials on the ECE software support pages here:

        http://eng.auburn.edu/programs/ece/students/computing-tutorials.html

Some additional MATLAB resources from Dr. Reeves (updated Jan. 2012):

Students can obtain my "Beginning MATLAB for Engineers" booklet at Engineering Duplicating Services.  I think it's around $3.

 

Also, remember that I've produced a collection of video tutorials on MATLAB basics, with topics from getting access to MATLAB at Auburn to writing your own m-file functions:

 

http://www.eng.auburn.edu/programs/ece/students/matlab-videos.html

 

 

Interesting STUFF

Help me out with some links to include here.

·        Stroke Victims Control Robotic Arm With Their Thoughts. (posted May 17, 2012 from ASEE First Bell)

·         IEEE Spectrum Online

·         “Why talking-to-text has taken off in China”  - BBC, May 31, 2012

·         “Is the end in sight for bucket-sized sodas?” – BBC, May 31, 2012