ECEN3300: Linear Systems (Signals and Systems)

 

Instructor: Prof. Shalom D. Ruben
TA: None
M,W,F 2-2:50PM
ECCR 155
Office: ECOT 438
Office Hours: Wed, Fri, 3-4pm

Characterization of linear and time-invariant systems in time and frequency domains. Continuous time systems are analyzed using differential equations and Laplace and Fourier transforms. Discrete time systems, which can be implemented using a modern digital signal processing framework, use difference equations, z-transforms and discrete time Fourier transforms for their analysis and design. Applications of linear systems include communications, signal processing, and control systems. (Prerequisite: ECEN 2260, Circuits as Systems)

Textbook

Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab, Signals & Systems, Second Edition, Prentice Hall, 1997, ISBN 0-13-814757-4.

Topics Covered (not restricted to this order)

  1. Continuous time (CT) and discrete time (DT) signals

  2. CT and DT linear and time-invariant (LTI) systems

  3. Time domain analysis of CT LTI systems

    1. Differential equations

    2. Unit impulse/step response

    3. Convolution

  4. Time domain analysis of DT LTI systems

    1. Difference equations

    2. Unit impulse/step response

    3. Convolution

  5. Transformed domain analysis of CT LTI systems

    1. Laplace transform, pole/zero plots

    2. Fourier transform, Fourier series

    3. System function and frequency response

  6. Transformed domain analysis of DT LTI systems

    1. z-transform, pole/zero plots

    2. DT Fourier transform, discrete Fourier series

    3. System function and frequency response

  7. Relationship between CT and DT signals, sampling theorem

  8. Relationship between CT and DT systems, step invariance, bilinear transformation

Grading Breakdowns

  1. Random Quizes (5%)

  2. Homework (20%)

  3. Midterms (20% each)

  4. Final (35%)

Aditional Material

  1. Differential Equations

  2. Difference Equations

Schedule (subject to change)

Week Date Topic Section in textbook
1 Jan 18 Syllabus and Math Review pp 71-72
2 Jan 23 CT and DT Signals 1.1-1.6
3 Jan 30 Linear-Time-Invariant (LTI) Systems 2.1-2.3,3.2
4 Feb 6 Differential and Difference Equations
CT Fourier Series
2.4
3.1-3.3,3.5
5 Feb 13 CT Fourier Series
CT Fourier Transform
3.3,3.5
4.1-4.7
6 Feb 20 DT Fourier Series
DT Fourier Transform
3.6,3.7
5.1-5.8
7 Feb 27 Midterm 1; Midterm1sol Chapters 1,2,3(not including DTFS),and 4
8 Mar 5 Time and Frequency Characterization 6
9 Mar 12 Sampling 7
10 Mar 19 Laplace
Transform
Laplace Handout 1
Laplace Handout 2
Laplace Handout 3
11 Mar 26 Spring Break
12 Apr 2 Midterm 2; Midterm 2 Sol DTFS, DTFT, Sampling
13 Apr 9 First and Second Order DT Systmes 5.8,6.6
14 Apr 16 Z-Transform 10, Z-Transform Handout
15 Apr 23 Discrete-Time System Rep
Block Diagram Manipulations
DT Sys Rep Handout(4.1-4.2)
Block Diagram Handout
16 Apr 30 Approximating Continuous-Time Controllers Emulations Handout (6.1)
May 4 Last Day of Classes

Homework

  1. Due on Monday at the start of class.

  2. Assignments must be neat, organized and legible. In plain English: If we cannot read your assignment, you will not get credit for it. Typed assignments are welcome.

  3. At the start of each problem, write out a brief description of the problem including given information and what is to be found. Put a box around all final answers.

  4. Show your work enough to fully demonstrate your understating and your arrival at your answer.

  5. Write on only one side of the paper. Pages must stapled be in order (i.e. following the order in which the problems were assigned).

  6. You only have TWO WEEKS from the return date to question the grading.

HW Problems Sol
1 1.2 (all), 1.21 (all), 1.34 (a,b,c), 1.46 (all) HW1sol (note that 1.21 (e) and (f) are wrong)
2 2.21(a,b,c), 2.24 (all), and
Write your own general conitinuous time convolution algorithm in Matlab
(use the example we did in class to check your code)
HW2sol
3 2.30, 2.32, 2.33 (a), 2.38 HW3sol
4 3.21, 3.22 (a)(i,iv), 4.23, 4.25 HW4sol
5 Redo the Midterm 1 Midterm1sol
6 3.26, 3.27, 3.32, 5.21(a-d), 5.27 HW6sol
7 6.33, 6.34, 7.21, 7.22, 7.26 HW7sol
8 HW8; Samples.mat HW8sol
9 HW9 HW9sol