ES 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 
Room 2005 
Tue & Thu 55:30 PM or by appt. 
(707) 6642030 
Course
Description: Lecture,
3 hrs. Analysis of linear timeinvariant systems, correlation, convolution,
impulse response, complex variables, Fourier series and transform, sampling,
filtering, modulation, stability and causality, feedback and control systems,
Laplace and Ztransform, 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, 1^{st} ed, Prentice Hall, 2003, ISBN 0201618540, 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 1hour Midterm and a 2hour
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
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
4.2 Inverse
4.3
4.4 Block Diagrams
4.5 From
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 ContinuousTime Signals
6.2 Convolution for Linear ContinuousTime Systems
6.3 Convolution of DiscreteTime Signals
6.4 Convolution for Linear DiscreteTime 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, 
10/7 
10/9 

10/14 
10/16 

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, PWSKent Publishing Company, 1989,
ISBN 053491568X.
·
“Signals &
Systems,” A. Oppenheim, A. WIllsky, 2^{nd}
ed., Prentice Hall, 1997, ISBN 0138147574.
·
MATLAB
Tutorial ◄
click here for the slides