Sonoma State UniversityES 400 (CES 400), Linear Systems Theory (3), Fall 2008

  

 Lectures & Labs

Lectures & Lab locations

Instructor

Office in Salazar Blg

Office hr (or by appt.)

Email

Tel

Lectures:

Tue & Thu 6 -7:15 PM

Salazar Blg. Room 2006

Dr. Ali Kujoory

Room 2005

Tue & Thu 5-5:30 PM

 or by appt.

ali.kujoory@ieee.org

(707) 664-2030

 

Course Description:  Lecture, 3 hrs. Analysis of linear time-invariant systems, correlation, convolution, impulse response, complex variables, Fourier series and transform, sampling, filtering, modulation, stability and causality, feedback and control systems, Laplace and Z-transform, fast Fourier transforms.

 

Course Objective:

·       To describe signals and how they are used in linear systems

·       To discuss various methods that can transform signal representations in time domain to their frequency domain representations

·       To examine simulation mechanism in solving  linear system problems

 

Prerequisite:  Math 241 (Differential Equation with Linear Algebra) or consent of instructor

 

Textbook:  “Linear Dynamic Systems and Signals,” Zoran Gajic, 1st ed, Prentice Hall, 2003, ISBN 0-20161854-0, TEXTBOOK.

 

Course Slides: We will go through the course slides available at http://www.sonoma.edu/users/k/kujoory in the class.  I urge you to download and review the slides before each class.  You are required to read the textbook after each class for further reinforcement.

 

Attendance: Attendance is mandatory.  There will be no excused absences except in the case of emergencies that could be substantiated.

 

Class Participation:  Your participation in the class and lab and the discussions are very important and would help me understand how much you follow the material.  As you go through the material before and after the class jot down your questions and ask me as I go through the slides.

 

Homework:  (see the list below) will be assigned weekly.

          Homework will include problems and exercises requiring MATLAB

          They provide an opportunity for you to learn the material and MATLAB applications (e.g. for simulations)

          Spend enough time to understand the problems by solving them

          I expect that you each do the homework & write the MATLAB codes you hand in, preferably electronically

          Use Wordpad, MS Words, Excel, or PowerPoint for electronic transmission

          Email your solutions to me by ali.kujoory@ieee.org no later than the beginning of the due session

          Be concise, neat, and organized.  There will be points for your presentation

          You can work in small groups

         Although each of you should workout and write your homework

         No copying please!

 

Exams:  A 1-hour Midterm and a 2-hour Final exam.  These exams are useful in motivating you to take your reading of the textbook and the slides seriously.

 

Grading Policy:  20% homework, 20% Lab, 20% Midterm, 40% final Exam

 

Academic Honesty:  You are responsible to behave ethically & honestly.  Copying, cheating, forgery, and other unethical or dishonest actions are not tolerated.  See http://www.sonoma.edu/uaffairs/policies/cheating_plagiarism.htm

 

My Expectations:

·         Always come to class prepared and on time to learn

·         Whenever for some critical reason you cannot attend, send me an email in advance

·         Read the slides before each lecture and the related chapter after the lecture

·         Reading the references deepens your understanding as a student

·         Hand in your assignments on time

·         Ask questions when you have them and contribute when you can

·         Have fun and look back on this as a positive and worthwhile course for your study and  career development

 

Course Outline (Unit numbers refer to the Chapters in the textbook):

 

1. Introduction to Linear Systems  ◄ click here for the slides

1.1 Continuous and Discrete Linear Systems and Signals

1.2 System Linearity

1.3 Mathematical Modeling of Systems

1.5 A Tutorial on MATLAB to be used in the course

Summary


2. Introduction to Signals  
◄ click here for the slides

2.1 Common Signals in Linear Systems

2.3 Signal Classification

2.4 MATLAB Laboratory Experiment on Signals

Summary

I. FREQUENCY DOMAIN TECHNIQUES

3. Part_1_Fourier_Series_and_Fourier_Transform ◄ click here for the slides

3. Part_2_Fourier_Series_and_Fourier_Transform  ◄ click here for the slides

3.1 Fourier Series

3.2 Fourier Transform and Its Properties

3.3 Fourier Transform in System Analysis

3.5 From Fourier Transform to Laplace Transform

3.6 Fourier Analysis MATLAB Laboratory Experiment

Summary

 

4. Part_1_Laplace_Transform  ◄ click here for the slides

4. Part_2_Laplace_Transform  ◄ click here for the slides

4.1 Laplace Transform and Its Properties

4.2 Inverse Laplace Transform

4.3 Laplace Transform in Linear System Analysis

4.4 Block Diagrams

4.5 From Laplace to the z-Transform

4.6 MATLAB Laboratory Experiment

Summary

 

5. Part_1_The_Z_Transform ◄ click here for the slides

5.1 The Z Transform and Its Properties

5.2 Inverse of the Z Transform

5.3 The Z Transform in Linear System Analysis

Summary

 

6. Convolution  ◄ click here for the slides

6.1 Convolution of Continuous-Time Signals

6.2 Convolution for Linear Continuous-Time Systems

6.3 Convolution of Discrete-Time Signals

6.4 Convolution for Linear Discrete-Time Systems

6.5 Numerical Convolution Using MATLAB

6.6 MATLAB Laboratory Experiments on Convolution

Summary

II. TIME DOMAIN TECHNIQUES

7. System Response in Time Domain  ◄ click here for the slides

7.1 Solving Linear Differential Equations

7.2 Solving Linear Difference Equations

Summary

 

Grading: 35% homework and MATHLAB applications, 25% midterm, 40% final Exam.

 

Tentative Schedule:

 

Tue

Thu

Topic/Unit

8/26

8/28

Welcome to the course, Introduction to Linear Systems

9/2

9/4

Introduction to Linear Systems & MATLAB

9/9

9/11

Introduction to Signals

9/16

9/18

Fourier Series and Fourier Transform

9/23

9/25

Fourier Series and Fourier Transform

9/30

10/2

Fourier Series and Fourier Transform, Laplace Transform

10/7

10/9

Laplace Transform

10/14

10/16

Laplace Transform

10/21

 

Midterm

 

10/23

The Z Transform

10/28

10/30

The Z Transform

11/4

11/6

Convolution

11/11

 

NO CLASS, Veteran’s Day

 

11/13

Convolution

11/18

11/20

Convolution

11/25

11/27

NO CLASS, Thanksgiving

12/2

12/4

System Response in Time Domain

12/9

12/11

Review, Q & A

12/16

 

Final Exam, 2 hrs (Covers all units)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Homework:  The homework problems are chosen from the textbook unless stated differently.

·         HW1:  Solve problems 1.1 a, 1.1c, 1.1d, 1.2, 1.6, & 1.14.      Due 5 PM, 

·         HW2:  Due 5 PM,

a)  Solve problems 2.4, 2.7a, 2.7c, 2.9, 2.18. For problems 2.4 and 2.9 mark the endpoints and use a domain of -5<k or x<6.

b)  Using MATLAB, draw sinc(x) for -5 < x < 5.  Hint:  See page 40 of the textbook.

·         HW3:  Solve problems 3.1, 3.3, 3.7a, 3.8a, 3.9a. Due 5 PM,  

·         HW4:  Solve problems 3.36, 3.58. Due 5 PM, 

·         HW5:  Solve problems 4.1, 4.4, 4.7a, 4.7d, 4.14c. Due 5 PM,

·         HW6: Solve problems 4.20a, 4.25c, 4.26a, 4.61. Due 5 PM, 

·         HW7: Solve problems 5.1, 5.5, 5.6, 5.8a. Due 5 PM, 

·         HW8: Solve problems 5.11a, 5.12b, 5.13c, 5.14a, 5.14b.  Also, use MATLAB to plot the system impulse response of Example 5.20 in the textbook (page 235).  Suppose that we do not have the discrete impulse function in our MATLAB version.   Due 5 PM,

·         HW9: Solve problems 6.4, 6.7b, 6.12, 6.27. Due 5 PM, 

·         HW10: Solve problems 7.2 for both f(t)=t^2 and f(t)= 5t+(t^2)(e^-t), 7.6b, 7.10a, 7.18a. Due 5 PM,

 

References: 

·         “A First Course in Differential Equations with Applications,” 4th ed. By Dennis Zill, PWS-Kent Publishing Company, 1989, ISBN 0-534-91568-X.

·         “Signals & Systems,” A. Oppenheim, A. WIllsky, 2nd ed., Prentice Hall, 1997, ISBN 0-13-814757-4.

·         MATLAB Tutorial  ◄ click here for the slides