Sonoma State UniversityES 400 (CES 400), Linear Systems Theory (3), Salazar 2009A, Fall 2008

  

Instructor

Office in Salazar Blg

Office hr

Email

Tel

Dr. Jagan Agrawal

Room 2004

Mon & Wed 2-3 PM & other days 10-11 AM or by appt.

jagan.agrawal@sonoma.edu

(707) 664-2030

Dr. Ali Kujoory

Room 2005

Mon 10:20-11:30 AM, 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.

 

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 Laplace Transform. 4.3 Laplace Transform in Linear System Analysis. 4.5 From Laplace to the z-Transform. 4.6 MATLAB Laboratory Experiment

 

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.