McMaster University

Electrical and Computer Engineering

ECE 3TP4  - Signals and Systems

 

Course Outline: 2004/2005, September 2004

 

Instructor: Dr. Mohamed Bakr, P.Eng., ITB A219, x24079, mbakr@mail.ece.mcmaster.ca

 

Teaching Assistants:

 

Jeff Bondy, jeff@soma.crl.mcmaster.ca

Kumar Punithkumar, punithan@grads.ece.mcmaster.ca

Nelson Costa, costa@soma.crl.mcmaster.ca

Abbas Ebrahimi-Moghadam, ebrahia@mcmaster.ca

Ningning Feng, fengn@mcmaster.ca

Peter Basl, baslpa@mcmaster.ca,

Payam Abolghasem, payam@grads.ece.mcmaster.ca

 

 

Lectures: Tuesday, 11:30am-12:20pm, ITB/AB102,

                   Thursday, 11:30am-12:20pm, ITB/AB102,

                     Friday, 11:30am-12:20am, ITB/AB102.

 

Tutorials: Wednesday 10:30am-11:20am, JHE/A102,

                     Wednesday 11:30 am-12:20 pm, JHE/A102.

 

Optional Tutorial: Monday 10:30 am-11:20am, T29/101

 

Course Objectives: To discover the fundamental principles of representing signals and linear systems in the time and frequency domains, and to use these principles in the analysis and design of linear control and communication systems.

 

Outline of Topics:

 

    Introduction (1 hour)

  • What are signals and systems? Examples from control and robotics, communications, remote sensing, biomedical, audio-visual entertainment.

 

    Elementary Signals and Basic Operations (2 hours)

  • Continuous-time and discrete-time; Periodic and non-periodic
  • Shifting and scaling
  • Sinusoidal signals; Complex exponentials; Impulse functions
  • Block diagrams
  • System properties: Stability, memory, causality, invertibility, time invariance, linearity

 

   Time Domain Representations of Linear Time-Invariant Systems (6 hours)

  • Convolution discrete-time and continuous-time; impulse response;
  • Stability and causality;
  • Frequency response;
  • Differential and difference equations;

 

    Fourier Representations of Signals (5 hours)

  • Definitions: Discrete-time Fourier Series, Fourier Series, Discrete-time Fourier Transform, Fourier Transform,
  • Properties: Symmetries, time-shift properties, convolution, modulation, Parseval, duality, time-bandwidth product

 

    Applications of Fourier Representations (4 hours)

  • Frequency response revisited, including differential/difference equations
  • Relationships between Fourier representations;
  • Basic concepts of filtering and filter design; Decibel measures
  • Case Study: A simplified DSB-SC transmission system
  • Sampling and ideal reconstruction of continuous-time signals; practical reconstruction;
  • Approximating the Fourier Transform using a Discrete-time Fourier Series of the sampled signal;

 

   Laplace Transform (4 hours)

  • Review of Laplace Transform: Definition, properties, poles and zeros
  • Region of convergence, inversion;
  • Application to systems analysis: Causality, stability, system inversion,
  • Relationships to differential equations and Fourier Transforms;
  • Fourier Transform from poles and zeros; Time domain response from poles and zeros.

 

  z-Transform (4 hours)

  • Complementary treatment to that for the Laplace transform

 

    Applications to Feedback Systems (9 hours)

  • Basic concepts of feedback
  • Open and closed loop control
  • Review of transient response of first and second-order systems; Reduced-order models
  • Stability: Root Locus; Nyquist Criterion; Bode Diagram;
  • Relative stability: Gain and phase margins; Damping ratio
  • Simple control system design; Proportional, integral, derivative, phase lag, phase lead

 

    Epilogue (1 hour)

  • Characteristics of physical signals
  • Characteristics of physical systems: Time-variation; Non-linearities;

 

Detailed Lectures Outline

 

Matlab Codes

 

Format: Three lectures and one official tutorial are offered per week. One optional tutorial is also offered to strengthen the students understanding of the subjects.  The course includes five laboratory experiments.  Students are expected to attend all course sessions.  Students must pass the final examination in order to pass the course.

 

Assessment: · 1 Midterm  20%, Thursday October 21st, 2004 @ 18:30 - 20:30

                           Rooms:  BIG-CM1-T28-001, BIG CM1-T29-105

                           ·  1 Midterm 20%, Thursday November 25th, 2004  @ 18:30 - 20:30

                           Rooms:   MDCL- 1309,  T29-105

                          ·  5 Laboratory Experiments  10%

                          ·  Final Examination           50%

 

Midterm1 Answers

 

First Midterm Results

 

Midterm2 Answers

 

Second Midterm Results

 

Total Semister Mark (out of 50)

 

Homeworks: Homeworks form an integral part of the course. They serve to strengthen and extend concepts covered in class. They also help you in your preparation for the labs, the quizzes, and ultimately the final exam. As such, it is crucial that you do them carefully and thoroughly. You are expected to do the homeworks by yourself. You can however consult with your classmates and discuss ideas. You can also ask me questions whenever you are stuck. The assigned problems/questions  will be given in class. Homeworks will not be graded, but it is your responsibility to make sure that you understand how to solve/answer the problems/questions. Homework answers/solutions will be posted at the beginning of the following week.

 

 

Formula Sheet

 

Chapter 1 Solutions

 

Chapter 2 Final Answers

 

Chapter 2 Detailed Answers

 

Chapter 3 Final Answers

 

Chapter 3 Detailed Answers

 

Chapter 4 Final Answers

 

Chapter 4 Detailed Answers

 

Chapter 5 Detailed Answers

 

Chapter 6 Answers

 

Chapter 6 Detailed Answers

 

Chapter 7 Answers

 

Chapter 8 Solutions

 

Chapter 8 Detailed Answers

 

Chapter 9 Solutions

 

Chapter 9 Detailed Answers

 

Chapter 11 Solutions

 

 

Laboratories: Labs Start on the week of September 27th

  • Lab 1: Representation of signals and systems in Matlab  (Monday September 27th-Friday October 8th)
  • Lab 2: Convolution: Impulse response, step response, frequency response. (Matlab) (Monday October 11th-Friday October 22nd)
  • Lab 3: Fourier Analysis and Filtering. (Monday October 25th-Friday November 5th)
  • Lab 4: Sampling. (Matlab) (Monday November 8th- Friday November 19th)
  • Lab 5: Control of a Servomechanism. (Monday November 22nd- Friday December 3rd)

 

Detailed Laboratory Instructions

 

Calculator requirement for tests and examinations: Only the McMaster standard calculator (Casio fx991) may is allowed in tests and examinations.

 

Resources: Signal Processing and Linear Systems, B.P. Lathi, Oxford University Press, 1998.

 

Policy Reminders:

 

            Senate and the Faculty of Engineering require all course outlines to include the following

 reminders:

 

“The Faculty of Engineering is concerned with ensuring an environment that is free of all adverse discrimination.  If there is a problem, that cannot be resolved by discussion among the persons concerned,  individuals are reminded that they should contact the Department Chair, the Sexual Harassment Officer or the Human Rights Consultant, as soon as possible.”

 

“Students are reminded that they should read and comply with the Statement on Academic Ethics and the Senate Resolutions on Academic Dishonesty as found in the Senate Policy Statements distributed at registration and available in the Senate Office.”

 

 

"Academic dishonesty consists of misrepresentation by deception or by other fraudulent means and can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads:  "Grade of F assigned for academic dishonesty"), and/or suspension or expulsion from the university.  It is your responsibility to understand what constitutes academic dishonesty.  For information on the various kinds of academic dishonesty please refer to the Academic Integrity Policy, specifically Appendix 3, located at
http://www.mcmaster.ca/senate/academic/ac_integrity.htm
 
The following illustrates only three forms of academic dishonesty:
 
1         Plagiarism, e.g. the submission of work that is not one's own or for which other credit has been obtained.  (Insert specific course information, e.g. style guide)
2         Improper collaboration in group work. (Insert specific course information)
3         Copying or using unauthorized aids in tests and examinations.
 
(If applicable) In this course we will be using a software package designed to reveal plagiarism.  Students will be required to submit their work electronically and in hard copy so that it can be checked for academic dishonesty."