ES 400 (CES 400), Linear Systems Theory (3), Salazar 2009A, Fall 2008
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Instructor |
Office in Salazar Blg |
Office hr |
Email |
Tel |
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Room 2004 |
Mon & Wed 2-3 PM & other days 10-11 AM or by appt. |
(707) 664-2030 |
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Room 2005 |
Mon 10:20-11:30 AM, Tue & Thu 5-5:30 PM or by appt. |
(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.
PREREQUISITE: Math 241
(Differential Equation with Linear Algebra) or consent of instructor
The objectives of this course are
to:
·
To
understand various forms of signals and how they are used in linear systems
·
To
learn various methods that can transform signal representations in time domain
to their frequency domain representations and vice-versa
·
To
learn transform techniques not related to time or frequency domains but useful
in solving linear systems problems
·
To
learn how to apply various transform techniques in solving linear systems
problems.
CLASS SCHEDULE:
·
Lectures:
Tuesdays and Thursdays, 6 to 7:15 PM. in Salazar #2006.
·
Lectures
for this course start on Tuesday, Aug. 26 and end on Thursday, Dec. 11.
·
No
classes on Nov. 11 (Veteran’s day) and Nov. 27 (Thanksgiving).
·
Nov.
18 and 20 classes to be rescheduled.
TEXTBOOK:
·
“Linear Dynamic Systems and Signals,” Zoran Gajic, 1st
ed, Prentice Hall, 2003, ISBN 0-20161854-0. Book Website: http://www.ece.rutgers.edu/~gajic/systems.html
·
“Continuous
and Discrete Signals,” Samir Soliman and Mandyam Srinath, 2nd
ed, Prentice Hall, 1998, ISBN 0-13-518473-8
COURSE SLIDES: We will go through the course slides available
at http://www.sonoma.edu/users/k/kujoory
and/or at http://www.sonoma.edu/users/a/agrawal/es400/
(prepared by Dr. Jingxian Wu). We urge you to download and review the slides
before each class. You are required
to read the textbooks after each class for further reinforcement. Note that the UserID/Password to access
both sites would be the same.
SOFTWARE: Matlab (Ver. 6.1 or later)
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.
COURSE SYLLABUS AND INSTRUCTION PLAN:
Lectures 1 to 3 (8/26, 8/28 &
9/2): Introduction to Linear Systems and
Signals (Chap. 1 “Introduction
to Linear Systems” & Chap 2 ”Introduction
to Signals”)
1.1
Continuous and Discrete Linear Systems and Signals. 1.2 System Linearity and
Time Invariance.
2.1 Common Signals
in Linear Systems. 2.2 Signal Operations. 2.3 Signal Classification. 2.4 MATLAB
Laboratory Experiment on Signals.
Lectures 4 to 7 (9/4, 9/9, 9/11,
9/16): Fourier Series and Fourier Transform
(Chap 3 “Part_1_Fourier_Series_and_Fourier_Transform”)
3.1
Periodic signals and functions, Fourier Series, signal representation in
trigonometric and exponential forms of Fourier Series, frequency and phase
spectra, signal power, examples.
Lectures 8 to 13 (9/18 & 9/23,
9/25, 9/30, 10/2 & 10/7): Fourier
Transform (Chapter 3) Part_2_Fourier_Series_and_Fourier_Transform”)
3.2
Aperiodic signals and functions, Fourier Series to Fourier Transform, analysis
of aperiodic signals using Fourier Transform, Fourier Transform of periodic
signals, continuous frequency and phase spectra, properties of Fourier
Transforms, inverse Fourier Transform, impulse response, concept of
convolution, its significance and applications, applications of Fourier
Transform properties, signal energy, Parseval’s theorem. 3.3 Fourier
Transform in System Analysis, Transfer Function, system response to periodic
inputs. 3.6 Fourier Analysis MATLAB Laboratory Experiment
Test #1: October 9 (Covers material from Lecture
#1 thru Lecture #13)
Lectures14 to 19 (10/14, 10/16,
10/21 & 10/23, 10/28 and 10/30): Laplace and Inverse Laplace Transforms (Chapter 4 “Part_1_Laplace_Transform”
& “Part_2_Laplace_Transform”)
4.1 From
Fourier Transform to Laplace Transform, definitions and existence conditions
for Laplace Transforms, properties of Laplace Transform, applications and
examples. 4.2 Inverse
Lectures 20 to 24 (11/4, 11/6,
11/13, 11/18 & 11/20): The Z-Transform (Chapter 5 “Part_1_The_Z_Transform”
& “Part_2_The_Z_Transform”)
5.1 The
Z-Transform and Its Properties. 5.2 Inverse of the Z-Transform. 5.3 The
Z-Transform in Linear System Analysis. 5.4 Block Diagram. 5.5 Discrete-Time
Frequency Spectra. 5.6 MATLAB Laboratory Experiment.
Test #2 on November 25 (Covers material from Lecture #14 thru
Lecture #24)
Lectures 25 to 27 (12/2 & 12/4
& 12/9): Linear
Controls Systems (Chapter 12 “Part_1_
Linear Control Systems”)
The Essence
of Feedback, open and closed loop systems, stability, transient and
steady-state system responses, system gain. Laboratory Experiment on Control
Systems.
Lecture 28 (12/11): Review of the course and final exam
Note: Chap 6 “Convolution”.provides
more information on Convolution (e.g., see Sections 6.1 to 6.4)
HOMEWORK PROBLEMS: The homework problems are chosen from the
textbook unless stated differently.
·
HW#1:
1.1(a,c,d), 1.2 and 1.3
·
HW
#2: Part
I: 2.4, 2.7(a,c), 2.9 and 2.18. for problems 2.4 and 2.18 mark the end points
and use a domain of -5 , k or x < 6.
Part II: Using MATLAB, draw sinc(x)
for -5 < x < 5. Hint: See page 40 of the text book.
·
HW
#3: 3.1, 3.3, and 3.6
·
HW
#4: 3.7(a), 3.11(a) and 3.14(a)
·
HW
#5: 3.13, 3.18, 3.24 and 3.26
·
HW
#6: 3.29, 3.41 and 3.42
·
HW
#7: Questions on Test #1
·
HW
#8: 4.3, 4.7(c)&(d), 4.9(c)&(d), and, 4.10
·
HW
#9: 4.11(a), 4.14(a), 4.17 and the following MATLAB Laboratory Experiments in
article 4.6 on page 191: Part 1(a) & (b), and, Part 2(a).
·
HW
#10: Solve from Zoran Gajic textbook problems
5.1, 5.5, 5.6, 5.8a, DUE 11/13
·
HW
#11: Solve from Zoran Gajic textbook 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), DUE 11/20
·
HW
#12: Solve from Zoran Gajic textbook problems 12.1,
12.2, 12.3, 12.4, and 12.6, DUE 12/9
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
REFERENCES:
·
“Continuous
and discrete signals and systems”, S.S. Soliman, M.D. Srinath, 2nd
Ed., Prentice Hall.
·
“Signals
& Systems,” A. Oppenheim, A. WIllsky, 2nd ed., Prentice
Hall, 1997, ISBN 0-13-
·
“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.
·
Tables
of Fourier, Laplace, and Z Transforms ◄ click here for the slides
·
MATLAB
Tutorial ◄ click here for the
slides
OUTCOMES: In this course, the students will attain:
·
an
ability to apply knowledge of mathematics, science, and engineering.
·
an
ability to design and conduct experiments, as well as to analyze and interpret
data.
·
an
ability to use the technique, skills, and modern engineering tools necessary
for engineering practice.
GRADING POLICY:
·
Homework
and project assignments 25%
·
Test
#1 (Thursday, Oct. 9) 25%
·
Test
#2 (Tuesday, Nov. 25) 25%
·
Final
Exam (Tuesday, Dec. 16, 8 to 9:50 PM) 25%
POLICY ON THE SUBMISSION OF HOMEWORK AND PROJECT WORK:
·
All
homework and projects must be done individually unless instructed
otherwise.
·
All
work must be submitted on 8.5 X11 papers and Tables and graphs in the homework
submissions must be presented neatly, properly labeled and must be clearly
explained.
·
Each
submission is due in the beginning of the class on the specified date.
Failing any of the above, a
submission may not be accepted resulting in the loss of grade in that
assignment.
DEADLINES TO DROP THE COURSE:
·
Last
day to drop with a ‘W’: Monday, September 22.
·
Last
day to petition to withdraw (because of serious and compelling reasons):
Friday, Nov. 7.