TORONTO METROPOLITAN UNIVERSITY

Course Outline (F2024)

ELE532: Signals and Systems I

Instructor(s)Dr. Soosan Beheshti [Coordinator]
Office: ENG425
Phone: (416) 979-5000 x 554906
Email: soosan@torontomu.ca
Office Hours: Wednesdays 12-1pm
Calendar DescriptionThis course deals with the analysis of continuous-time and discrete-time signals and systems. Topics include: representations of linear time-invariant systems, representations of signals, Laplace transform, transfer function, impulse response, step response, the convolution integral and its interpretation, Fourier analysis for continuous-time signals and systems and an introduction to sampling.
PrerequisitesCEN 199, COE 428, ELE 404, MTH 314
Antirequisites

None

Corerequisites

None

Compulsory Text(s):
  1. B.P. Lathi, Linear Systems and Signals, 3rd edition, Oxford University Press, 2018.
  2. Laboratory MATLAB assignment descriptions and procedures, and assignment problems are available from the course home page on D2L Brightspace via my.torontomu.ca.
Reference Text(s):
  1. M. J. Roberts, Signals and Systems: Analysis Using Transform Methods and MATLAB, McGraw Hill, 2004.
  2. Signals and Systems, A.V. Oppenheim, A.S. Willsky, S.H. Nawab, 2nd edition, Pearson, 1997.
Learning Objectives (Indicators)  

At the end of this course, the successful student will be able to:

  1. - Learn the properties of linear time-invariant (LTI) systems. - Learn time-domain and frequency-domain analysis of continuous-time signals and LTI systems. - Learn analog-to-digital and digital-to-analog conversion techniques. (1b)
  2. - Learn mathematical foundations of frequency- domain analysis techniques (Fourier series, Fourier transform, Laplace transform) applicable to continuous-time signals and systems. (1c)
  3. - Determine system output for a given input signal using time and frequency-domain techniques. - Learn to select the most appropriate and efficient solution technique based on the information and mathematical models provided. - Identify system characteristics required to shape and modify signal characteristics such as in filtering and relate these characteristics to system parameters. (2b)
  4. Learn frequency analysis of continuous-time signals and LTI systems and describe differences between Fourier transform and Fourier series analysis. Perform both Fourier transform and Fourier series in hypothetical design and analysis of signals and LTI systems. Analyze the result of the evaluation to detect if a continuous-time system is Linear Time-Invariant (LTI). To discern additional criteria. In case the system is LTI, an additional characteristic of the system (impulse response of the system) is calculated to facilitate calculation and evaluation of the system's output. (4b)
  5. - Uses Matlab/Simulink as a signal analysis, simulation and visualization tool. - Generates system models using simulation tools to verify system properties and perform signal operations. (5a)
  6. Read and appropriately respond to technical and non-technical written instructions. Cites evidence to construct and support an argument. Produce four lab reports using appropriate format, grammar, and citation styles for technical and non-technical audiences. (7a)
  7. Illustrate concepts of continuous-time signals and systems through the graphical presentation of their properties. (7c)
  8. Finding the relationship between signals, building a signal based on other existing bases, signal modulation, and its practical issues that can be well explained with the theory. (12a)

NOTE:Numbers in parentheses refer to the graduate attributes required by the Canadian Engineering Accreditation Board (CEAB).

Course Organization

3.0 hours of lecture per week for 13 weeks
2.0 hours of lab per week for 12 weeks
0.0 hours of tutorial per week for 12 weeks

Teaching Assistants Iqbal Banwait, iqbal.banwait@torontomu.ca
 Khashayar Bayati, khashayar.bayati@torontomu.ca
 Seungho Choe, seungho.choe@torontomu.ca
 Lucas Krome, lucas.krome@torontomu.ca
 Eric Levy, eric.j.levy@torontomu.com
 Luella Marcos, lgmarcos@torontomu.ca
 Brendan Wood, bwood06@torontomu.ca
 Xiaodan Bi xiaodan.bi@torontomu.ca
  
 
Course Evaluation
Theory
Quizzes (4 X 6.25%) 25 %
Midterm Examination 25 %
Final Examination 30 %
Laboratory
Laboratory Assignments (4 X 5%) 20 %
TOTAL:100 %

Note: In order for a student to pass a course, a minimum overall course mark of 50% must be obtained. In addition, for courses that have both "Theory and Laboratory" components, the student must pass the Laboratory and Theory portions separately by achieving a minimum of 50% in the combined Laboratory components and 50% in the combined Theory components. Please refer to the "Course Evaluation" section above for details on the Theory and Laboratory components (if applicable).


Examinations- Quizzes are scheduled on Week 3, 5, 10 and 12, approximately 50 minutes, during the regular lecture hours (the first hour): Quiz 1 on September 19, Quiz 2 on October 3, Quiz 3 on November 7 Quiz 4 on November 21.
 
 - Midterm Exam is in Week 7, on Thursday October 17, two and half hours, problem-solving, during the regular lecture hours (covers Weeks 1-6 of lecture notes).
 
 - Final Exam is scheduled during the Fall 2024 term undergraduate exam period (covers Weeks 1-13 with emphasis on Weeks 6, 8-13 of lecture notes).
 
Other Evaluation Information- Practice Problems/Assignments: Assignment problems and solutions will be provided on D2L.The assignments will neither be collected nor graded; they are provided only as a study guide. You are strongly recommended to attempt to solve the problems on your own without looking at the solutions first. If you have any questions about an assignment problem or its solution, please consult the course instructor or the teaching assistant during their consulting hours.
 
 - The lab marks are based on attendance, successful completion of pre-lab problems, participation, and completion of experiment steps, lab interviews, and lab reports. Students will have the responsibility to achieve a working knowledge of the software packages that will be used in the lab. Students will work in groups of two.
 
 
 
Teaching MethodsIn person lectures are in ENG103 Thursdays 3-6pm  
Other InformationPDF version of the lecture notes will be posted before the lecture.

Course Content

Week

Hours

Chapters /
Section

Topic, description

1 & 2

6

Signals and Systems Representations
 Size of a signal: signal energy and power useful signal operations: time-shifting, time scaling, time reversal, combined operations, classification of signals: linear systems, time-invariant systems, linear and time-invariant continuous-time (LTIC) systems, useful signal models: unit step function, unit impulse function, exponential function, even and odd functions, continuous-time systems, classification of systems, internal and external descriptions of a system.
 (Reference: Chapter 1 Sections 1.1-1.7)


3-5

9

Time-Domain Analysis of Continuous-Time Systems
 System response to internal conditions: the zero-input response, the unit impulse response, system response to external response: zero-state response, the convolution integral, interconnected systems, total system response, classical solution to differential equations: forced responsethe method of undetermined coefficients, system stability: internal (asymptotic) stability, BIBO stability, criterion relationship between BIBO and asymptotic stability, intuitive insights into system behavior.
 (Reference: Chapter 2 Sections 2.1-2.6 and 2.8-2.9)


7

3

Midterm Exam


6 & 8

6

Continuous-Time Signal Analysis: The Fourier Series
 Periodic signal representation by trigonometric Fourier series existence and convergence of Fourier series exponential Fourier series LTIC system response to periodic inputs.
 (Reference: Chapter 6 Sections: 6.1-6.4)


9 & 10

6

Continuous-Time Signal Analysis: The Fourier Transform
 Aperiodic signal representation by Fourier integral Fourier transforms of some useful functions properties of the Fourier transform signal transmission through LTIC systems ideal and practical filters signal energy application to communications.
 (Reference: Chapter 7 Sections 7.1-7.9)


11

3

Sampling: Discrete-Time Signals
 Introduction to Sampling theorem signal reconstruction.
 (Reference: Chapter 8 Sections 8.1-8.2)


12 & 13

6

The Laplace Transform
 The Laplace transforms, properties of the Laplace transform, solution of differential equations: zero-state response, stability, inverse systems, analysis of electric networks, block diagrams, system realizations, application to feedback and control, the frequency response of an LTIC system.
 (Reference: Chapter 4 Sections 4.1-4.2 & 4.4-4.6)


Laboratory(L)/Tutorials(T)/Activity(A) Schedule

Week

L/T/A

Description

2

L/T

Lab0: Tutorial Introduction to Matlab
 It is very important to attend the Matlab tutorial scheduled for Week 2.

3 &4

L/T

Tutorial & Lab Experiment 1: Signal and System Representations
 In this experiment you will work with simple Matlab functions and will
 explore some signals properties
 

5 & 6

L/T

Tutorial & Lab Experiment 2: Time-Domain Analysis of Continuous-Time
 Systems. In this experiment you will learn how to use M-files in Matlab and
 exercise convolution and system properties

7

T

Tutorial
 Problems from course textbook and quizzes will be discussed.

8 & 9 &10

L/T

Tutorial & Lab Experiment 3: The Fourier Series
 The purpose of this experiment is to investigate the Fourier Series while
 continuing to learn how to use Matlab effectively. General Fourier series
 characteristics will be investigated and Matlab functions that work with
 Fourier series will be developed. Also the effects on the Fourier series
 coefficients due to changing the period of a periodic signal will be
 investigated along with the effects of series truncation on signal
 reconstruction.

11 & 12

L/T

Tutorial & Lab Experiment 4: The Fourier Transform
 In this experiment you will investigate properties of the Fourier transform.
 You will use Fourier Transform to analyze dual-tone multi frequency
 (DTMF) signals used in telephone signalling.

13

T

Tutorial: Problems from course textbook and quizzes will be discussed

University Policies & Important Information

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