Dr. Ellen Gethner

CSC 3645, Discrete Linear Systems (Fall 2007)

Syllabus

automatically updated on 4th September 2007

  1. Class meets in NC 1204 until you hear otherwise
  2. The Student Webpage is up and running. If you have trouble logging in, contact Kyle at dagnarus75 at gmail dot com.
  3. Send a recognizable digital photo of yourself to Kyle at dagnarus75 at gmail dot com from your preferred e-mail address by Friday, 31 August 2007.

[ Instructor | Class Time and Room | Textbooks and Resources | Prerequisites | Objective | Quizzes, Homework, Exams | Schedule | Student Page | Academic Deadlines (pdf) ]

Instructor

Dr. Ellen Gethner
Email: ellen dot gethner at cudenver edu
Office: North Classroom 2604-A3
Phone: (303) 556 2358 (Use at your own risk)
Office hours: 4:00-5:00pm and 8:15-9:15pm M, W; 11:30am-12:30pm Tues (and by appointment)

Class Time and Room

Mondays and Wednesdays 5:30-6:45pm, North Classroom 1204
We will also meet on announced Mondays in the Raytheon lab to do Mathematica labs and tutorials.

Textbooks and Other Resources

There is no required textbook: we will use class notes and a variety of websites.

Here are the sources from which I compile my lecture notes:

  1. Linear System Theory and Design (3rd edition) by Chi-Tsong Chen
  2. Structure and Interpretation of Signals and Systems by Edward Lee and Pravin Varaiya
  3. Linear Systems and Signals by B.P. Lathi
  4. Signals and Systens by Alan Oppenheim and Alan Willsky
  5. Signals and Systems; Continuous and Discrete by Ziemer, Tranter and Fannin

A Few Web Resources (please send me others that you find useful)

  1. Very Brief Summary of Linear Systems
  2. Very Long Summary of Linear Systems (pdf) This has much more content than we will cover in CSC 3645.
  3. CT Signals (pdf)
  4. DT Signals (pdf)
  5. Relation between Impulse Response and Frequency Response: A Matlab Tutorial
  6. Listen to Fourier Series Java Applet
  7. Linear Time Invariant Systems (tutorial)

Prerequisites

MATH 3195 (Linear Algebra and Differential Equations) and CSC 2142 (Circuit Analysis II). Each student must sign and return a prerequisite agreement form to receive any credit for any assignment or exam. If this form is not returned by the 3rd week, the student will be administratively dropped from the course.

Course Objective

Grades and Policies (VERY IMPORTANT)

Course Schedule and Outline


We will study the following topics (the instructor may choose to add to and/or subtract from the list of topics as the semester progresses):

Schedule (subject to change)
Week # Date Topic Reading/Comments Assignments Criteria a-k
Week 1 August 20 and 22 Overview of Systems and Signals Class Notes a,b,c,e,g,i
Week 2 August 27 and 29 Mathemematical Descriptions of Signals, especially unit step, ramp, and unit impulse functions. Relations among the three in terms of integration and differentiation. Class Notes a,b,c,e,g,i
Week 3 Sep. 3 (no class) and Sep. 5 Continuous-time signals continued: Sampling, Equivalence, and Scaling Properties of impulse functions. Class Notes a,b,c,e,g,i
Week 4 Sep. 10 and 12 Continuous-time signals continued. Examples. Composition of continuous-time functions: time scaling and time shifting and amplitude change. Other transformations of continuous-time functions: differentiation and integration. Begin searching for patterns in signal processing functions: Even, odd, and periodic functions. Class Notes a,b,c,e,g,i
Week 5 Sep. 17 and 19 Even, odd, and period functions continued. Begin Discrete-Time functions. Method of sampling to attain the DT counterpart of a CT function. Similarities and differences among some of the DT and CT analogies. Examples of DT singuarity functions, sinusoids, and complex exponentials. Class Notes a,b,c,e,g,i
Week 6 Sep. 24 and 26 More on periodic functions; signal engery and power; DT functions that are the anologies to the singularity functions (such as unit step and unit ramp funcitons); amplitude scaling, compression and expansion; DT analogy for Even and Odd functions; Intro to systems: BIG example by way of a simple circuit Class Notes a,b,c,e,g,i
Week 7 Oct. 1 and 3 Introduction to Systems: Tuning fork example, systems terminology (excitation, response, SISO, MIMO, SIMO, memoryless, causal, distributed, lumped). Begin work on Linear Systems, and Linear Time Invariant (LTI) Systems. Terms used: additivity, homogeneity, superposition, state vector, initial state vector, zero-state response, zero-input response, relaxed, impulse response function, impulse response matrix, state-space description. Class notes a,b,c,e,g,i
Week 8 Oct. 8 and 10 To be announced Class Notes a,b,c,e,g,i
Week 9 Oct. 15 and 17 MIDTERM EXAM IN CLASS ON Monday October 15; returned and reviewed on Wednesday You may bring one 8.5 x 11" sheet of paper (both sides) with any notes you wish to bring into the exam. a,b,c,e,g,i
Week 10 Oct. 22 and 24 Unity feedback example of a SISO system; state space model of Discrete Linear Systems and the [A,B,C,D] matrix representation of such a system; examples include echo effect and moving average, Discrete LTI impulse response, bank balance models Class notes a,b,c,e,g,i
Week 11 Oct. 29 and 31 The effect of an LTI system on general sinusoidal functions; meta-examples (audio equalizer and image processing); Discrete-time frequency response; finding and using DT frequency response; Filter example with four sub-examples class notes a,b,c,e,g,i
Week 12 Nov. 5 and 7 Fourier Series and Fourier Transform; constructing the Fourier Series of an image; Fourier Roadmap Class notes a,b,c,e,g,i
Week 14 Nov. 12 and 14 Fourier Coefficients computations; relation between Discrete Fourier Series (DFS) and Discrete Fourier Transform (DFT); Discrete Square Wave Example; Mini-Characterization of DT Signals (toward an unerstanding of the Fourier Transform and its relation to LTI systems) Class Notes a,b,c,e,g,i
Week 13 Nov. 19-25 Fall Break Happy Thanksgiving! a,b,c,e,g,i
Week 14 Nov. 26 and 28 Fourier Transform of Periodic Signals; More properties of Fourier Transform: time shifting, frequencey response, impulse response; FFT of constant signal versus FFT of pulse and impulse Class Notes a,b,c,e,g,i
Week 15 Dec. 3 and 5 Frequency shifting and modulation; Laplace and Z-tranforms (what to do when the FT does not exist), shapes of regions of convergence, computational examples, Pole and Zeros plots Class Notes a,b,c,e,g,i
Week 16: FINALS WEEK FINAL EXAM to be determined by registrar. Closed book and notes. You may bring one 8.5 x 11" sheet of paper (both sides) with any notes you wish to bring into the exam.