TORONTO METROPOLITAN UNIVERSITY

Course Outline (W2024)

ELE532: Signals and Systems I

Instructor(s)Dr. Alagan Anpalagan [Coordinator]
Office: ENG447
Phone: (416) 979-5000 x 556079
Email: alagan@torontomu.ca
Office Hours: Tuesdays 12 noon -1 pm
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 AssistantsIqbal Banwait (iqbal.banwait@torontomu.ca@torontomu)
Course Evaluation
Theory
Quizzes (3 X 5%) 15 %
Midterm Examination 25 %
Final Examination 40 %
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 as indicated on the course webpage or course management sheet during the lab hours. Duration is 30 minutes. Closed-book/notes.
 
 - Midterm Exam will be held as indicated on the course webpage or course management sheet, during the regular lecture hours. It is closed-book/notes 2.5 hour exam, problem-solving.
 
 - Final Exam is scheduled during the Winter 2024 term undergraduate exam period. It is cumulative. it is a closed-book/notes 3-hour exam. An aid sheet will be provided.
 
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, i.e., MATLAB. Students will work in groups of two.
 
 - Lab assignments (1-4) are available in Labs folder in D2L.
 - Lab reports (pdf file) should be submitted (one per group) in Assessments->Assignments folder before the deadline.
 
 - Quizzes will be held on the announced date approximately during the last 30 minutes.
Teaching MethodsThe weekly lecture time will be dedicated to introducing and discussing in detail the concepts, and providing live examples of the theoretical materials in the posted lecture notes.
Other InformationPDF version of the lecture notes will also be posted.
 

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

Study Week (No lectures, No labs)


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

3

Midterm Exam


10 & 11

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)


12

3

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


13 &14

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 and 4.6)


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

Week

L/T/A

Description

2

L

LAB 0: Matlab Introduction

3

L

Lab1:  Working with Matlab Functions, Visualization of Signals, and Signal Properties

4

L/T

Lab1 / Tutorial
 QUIZ #1
 Lab Assignment #1 Due

5

L

Lab2: System Properties & Convolution

6

L

Lab2

8

L/T

Lab2 / Tutorial
 QUIZ #2
 Lab Assignment #2 Due

9

L

Lab3: Fourier Series Analysis using Matlab

10

L

Lab3

11

L/T

Lab3 / Tutorial
 Lab Assignment #3 Due

12

L

Lab4: Fourier Transform: Properties and Applications

13

L

Lab4
 Quiz #3

14

L

Lab4
 Lab Assignment #4 Due

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