Course Outline (W2023)

ELE632: Signals and Systems II

Instructor(s)Dr. Dimitri Androutsos [Coordinator]
Office: ENG 472
Phone: 555334 / 556104
Office Hours: TBA
Calendar DescriptionThe topics covered in the course includes a general discussion on discrete signals (periodic signals, unit step, impulse, complex exponential), a general discussion on discrete systems, Discrete-Time Fourier Series (DTFS), Discrete-Time Fourier Transform (DTFT); analysis and synthesis, Fourier Spectra; continuous nature, periodicity, existence, Properties of the DTFT; linearity, conjugation, time/frequency reversal, time/frequency shifting, etc. LTI discrete time system analysis using DTFT, DTFT and Continuous-Time FT comparison and relation, DFT and FFT discussion and their relation to DTFT and CTFT, Discrete-Time Sampling, Z-Transform; generalization of the DTFT.
PrerequisitesELE 532




Compulsory Text(s):
  1. B.P. Lathi, Linear Systems and Signals, 3rd edition, Oxford University Press, 2018.
Reference Text(s):
  1. M. J. Roberts, Signals and Systems, 2nd edition, McGraw Hill, 2011.
Learning Objectives (Indicators)  

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

  1. Learn mathematical foundations of frequency-domain analysis techniques (Discrete-Time Fourier series, Discrete-Time Fourier transform, z-transform) applicable to discrete-time signals and systems. Learn the mathematical relations and mapping between continuous-time and discrete-time techniques. (1b)
  2. Learn properties of discrete-time, linear time-invariant (LTI) systems. Learn time-domain and frequency-domain analysis of discrete-time signals and systems. Learn the differences between continuous-time and discrete-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 (pole-zero locations). (2b)
  4. Applies engineering principles to analyze signals using time- and frequency-domain techniques, identifies signal parameters (bandwidth, signal-to- noise ratio) including potential distortion components at various points within a signal processing model. Uses analyzed and measured signal characteristics to formulate discrete-time systems to shape signal (e.g. filtering, elimination of distortion components) Develops software to implement the required signal shaping Measures the effectiveness of the design by testing it with test signals. (4b)
  5. Use Matlab/Simulink as a signal analysis, simulation and visualization tool. Generate 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 five lab reports using appropriate format, grammar, and citation styles for technical and non-technical audiences. (7a)
  7. Illustrate concepts of discrete-time signals and systems through graphical presentation of their properties. (7c)
  8. Finding relationship between signals, building a signal based on other existing basis, digital signal processing 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 AssistantsTBA
Course Evaluation
Midterm Exam 25 %
Quizzes (4 X 3.75) 15 %
Final Exam 40 %
Lab Assignments 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).

ExaminationsMidterm exam in Week 7 (right after reading week), two hours, (covers Weeks 1-6).
Other Evaluation InformationPractice Problems/Assignments:  
 Assignment problems and their solutions will be provided on D2L. These 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 question about an assignment problem or its respective solution, please consult the course instructor or the teaching assistant during their consulting hours.
 Lab assignments:
 Lab marks are based on completion of assignments.  Students will have the responsibility to achieve a working knowledge of the software package that will be used for the lab assignments.  Students will work individually.
Teaching MethodsAll lectures will be recorded and posted as well as the instructor's notes.
Other InformationCourse Twitter account: @RU_ele632
 Instructor Twitter account: @EngProfD

Course Content



Chapters /

Topic, description



Chp 3 Sect 1-3

Introduction to discrete-time systems and signals. Important signals and operations.



Chp 3 Sect 3-4

Time domain analysis of discrete time systems:  linearity, time-invariance, causality, memory



Chp 3 Sect 4-6

Classification of discrete systems system equations system response to internal conditions.



Chp 3 Sect 7-8

Impulse Response and Convolution. Interconnected Systems.



Chp 3 Sect 8-9, Chapter 9, Sect 1

More convolution; Stability; Discrete-Time Fourier Series (DTFS) intro.



Chp 9 Sect 1-2

Discrete-Time Fourier Series (DTFS)



Chp 9 Sect 2

Discrete-Time Fourier Transform (DTFT)



Chp 5 Sect 2--54

DTFT properties, system analysis, filters.



Chp 8 Sect 4-6

Spectral Sampling,the DFT, DFT properties and applications, zero-padding, the FFT.



Chp 5 Sect 1,2,3

z-Transform intro; Inverse z-Transform; z-Transform properties, difference equations.



Chp 9 Sect 5,6,8

Frequency response; pole-zero analysis; stability;



Chp 9 Sect 4,6,8

Regions-of-Convergence; Bilateral z-Transform;z-Transform system realization

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






LAB ASSIGNMENT 0:  Introduction



LAB ASSIGNMENT 1: Time-Domain Analysis of Discrete-Time Systems-Part 1



LAB ASSIGNMENT 2: Time-Domain Analysis of Discrete-Time Systems-Part 2



LAB ASSIGNMENT 3 Discrete-Time Fourier Series



LAB ASSIGNMENT 4: Discrete Time Fourier Transform



LAB ASSIGNMENT 5: Sampling and Discrete Fourier Transform

Policies & Important Information:

Students are reminded that they are required to adhere to all relevant university policies found in their online course shell in D2L and/or on the Senate website

  1. In accordance with the Policy on TMU Student E-mail Accounts (Policy 157), Toronto Metropolitan University (TMU) requires that any electronic communication by students to TMU faculty or staff be sent from their official university email account;
  2. Any changes in the course outline, test dates, marking or evaluation will be discussed in class prior to being implemented;
  3. Assignments, projects, reports and other deadline-bound course assessment components handed in past the due date will receive a mark of ZERO, unless otherwise stated. Marking information will be made available at the time when such course assessment components are announced.
  4. Familiarize yourself with the tools you will need to use for remote learning. The Continuity of Learning Guide for students includes guides to completing quizzes or exams in D2L or Respondus, using D2L Brightspace, joining online meetings or lectures, and collaborating with the Google Suite.
  5. The University has issued a minimum technology requirement for remote learning. Details can be found at: Please ensure you meet the minimum technology requirements as specified in the above link.
  6. Toronto Metropolitan University COVID-19 Information and Updates (available for Students summarizes the variety of resources available to students during the pandemic.
  7. Refer to our Departmental FAQ page for information on common questions and issues at the following link:

Missed Classes and/or Evaluations

When possible, students are required to inform their instructors of any situation which arises during the semester which may have an adverse effect upon their academic performance, and must request any consideration and accommodation according to the relevant policies as far in advance as possible. Failure to do so may jeopardize any academic appeals.

  1. Academic Consideration Requests for missed work (e.g. missing tests, labs, etc) - According to Senate Policy 134, Section 1.2.3, if you miss any exams, quizzes, tests, labs, and/or assignments for health or compassionate reasons you need to inform your instructor(s) (via email whenever possible) in advance when you will be missing an exam, test or assignment deadline. When circumstances do not permit this, you must inform the instructor(s) as soon as reasonably possible". In the case of illness, a Toronto Metropolitan Student Health Certificate, or a letter on letterhead from an appropriate regulated health professional with the student declaration portion of the Student Health Certificate attached. For reasons other than illness, proper documentation is also required (e.g. death certificate, police report, TTC report). ALL supporting documentation for illness or compassionate grounds MUST be submitted within three (3) working days of the missed work." NOTE: You are required to submit all of your pertinent documentation through the University's online Academic Consideration Request system at the following link:
  2. Religious, Aboriginal and Spiritual observance - If a student needs accommodation because of religious, Aboriginal or spiritual observance, they must submit a Request for Accommodation of Student Religious, Aboriginal and Spiritual Observance AND an Academic Consideration Request form within the first 2 weeks of the class or, for a final examination, within 2 weeks of the posting of the examination schedule. If the requested absence occurs within the first 2 weeks of classes, or the dates are not known well in advance as they are linked to other conditions, these forms should be submitted with as much lead time as possible in advance of the absence. Both documents are available at If you are a full-time or part-time degree student, then you submit the forms to your own program department or school;
  3. Academic Accommodation Support - Before the first graded work is due, students registered with the Academic Accommodation Support office (AAS - should provide their instructors with an Academic Accommodation letter that describes their academic accommodation plan.

Virtual Proctoring Information (if used in this course)

Online exam(s) within this course may use a virtual proctoring system. Please note that your completion of any such virtually proctored exam may be recorded via the virtual platform and subsequently reviewed by your instructor. The virtual proctoring system provides recording of flags where possible indications of suspicious behaviour are identified only. Recordings will be held for a limited period of time in order to ensure academic integrity is maintained and then will be deleted.

Access to a computer that can support remote recording is your responsibility as a student. The computer should have the latest operating system, at a minimum Windows (10, 8, 7) or Mac (OS X 10.10 or higher) and web browser Google Chrome or Mozilla Firefox. You will need to ensure that you can complete the exam using a reliable computer with a webcam and microphone available, as well as a typical high-speed internet connection. Please note that you will be required to show your Toronto Metropolitan University OneCard prior to beginning to write the exam. In cases where you do not have a Toronto Metropolitan University OneCard, government issued ID is permitted.

Information will be provided prior to the exam date by your instructor who may provide an opportunity to test your set-up or provide additional information about online proctoring. Since videos of you and your environment will be recorded while writing the exam, please consider preparing the background (room / walls) so that personal details are not visible, or move to a room that you are comfortable showing on camera.

Academic Integrity

Toronto Metropolitan University's Policy 60 (the Academic Integrity policy) applies to all students at the University. Forms of academic misconduct include plagiarism, cheating, supplying false information to the University, and other acts. The most common form of academic misconduct is plagiarism - a serious academic offence, with potentially severe penalties and other consequences. It is expected, therefore, that all examinations and work submitted for evaluation and course credit will be the product of each student's individual effort (or an authorized group of students). Submitting the same work for credit to more than one course, without instructor approval, can also be considered a form of plagiarism.

Suspicions of academic misconduct may be referred to the Academic Integrity Office (AIO). Students who are found to have committed academic misconduct will have a Disciplinary Notation (DN) placed on their academic record (not on their transcript) and will normally be assigned one or more of the following penalties:

  1. A grade reduction for the work, ranging up to an including a zero on the work (minimum penalty for graduate work is a zero on the work);
  2. A grade reduction in the course greater than a zero on the work. (Note that this penalty can only be applied to course components worth 10% or less, and any additional penalty cannot exceed 10% of the final course grade. Students must be given prior notice that such a penalty will be assigned (e.g. in the course outline or on the assignment handout);
  3. An F in the course;
  4. More serious penalties up to and including expulsion from the University.

The unauthorized use of intellectual property of others, including your professor, for distribution, sale, or profit is expressly prohibited, in accordance with Policy 60 (Sections 2.8 and 2.10). Intellectual property includes, but is not limited to:

  1. Slides
  2. Lecture notes
  3. Presentation materials used in and outside of class
  4. Lab manuals
  5. Course packs
  6. Exams

For more detailed information on these issues, please refer to the Academic Integrity policy( and to the Academic Integrity Office website (

Academic Accommodation Support

Toronto Metropolitan University acknowledges that students have diverse learning styles and a variety of academic needs. If you have a diagnosed disability that impacts your academic experience, connect with Academic Accommodation Support (AAS). Visit the AAS website or contact for more information.

Note: All communication with AAS is voluntary and confidential, and will not appear on your transcript.

Important Resources Available at Toronto Metropolitan University

  1. The Library provides research workshops and individual assistance. If the University is open, there is a Research Help desk on the second floor of the library, or students can use the Library's virtual research help service at to speak with a librarian.

  2. Student Life and Learning Support offers group-based and individual help with writing, math, study skills, and transition support, as well as resources and checklists to support students as online learners.

  3. You can submit an Academic Consideration Request when an extenuating circumstance has occurred that has significantly impacted your ability to fulfill an academic requirement. You may always visit the Senate website and select the blue radial button on the top right hand side entitled: Academic Consideration Request (ACR) to submit this request).

    Please note that the Provost/Vice President Academic and Deans approved a COVID-19 statement for Fall 2022 related to academic consideration. This statement will be built into the Online Academic Consideration System and will also be on the Senate website ( in time for the Fall term:

    Policy 167: Academic Consideration for Fall 2022 due to COVID-19: Students who miss an assessment due to cold or flu-like symptoms, or due to self-isolation, are required to provide a health certificate. All absences must follow Senate Policy 167: Academic Consideration.

    Also NOTE: Policy 167: Academic Consideration does allow for a once per term academic consideration request without supporting documentation if the absence is less than 3 days in duration and is not for a final exam/final assessment. If the absence is more than 3 days in duration and/or is for a final exam/final assessment, documentation is required. For more information please see Senate Policy 167: Academic Consideration.

  4. TMU COVID-19 Information and Updates for Students summarizes the variety of resources available to students during the pandemic.

  5. TMU COVID-19 Vaccination Policy.

  6. If taking a remote course, familiarize yourself with the tools you will need to use for remote learning. The Remote Learning guide for students includes guides to completing quizzes or exams in D2L Brightspace, with or without Respondus LockDown Browser and Monitor, using D2L Brightspace, joining online meetings or lectures, and collaborating with the Google Suite.

  7. Information on Copyright for students.

  8. At Toronto Metropolitan University (TMU), we recognize that things can come up throughout the term that may interfere with a student's ability to succeed in their coursework. These circumstances are outside of one's control and can have a serious impact on physical and mental well-being. Seeking help can be a challenge, especially in those times of crisis.

    If you are experiencing a mental health crisis, please call 911 and go to the nearest hospital emergency room. You can also access these outside resources at anytime:

    If non-crisis support is needed, you can access these campus resources:

    We encourage all Toronto Metropolitan University community members to access available resources to ensure support is reachable. You can find more resources available through the Toronto Metropolitan University Mental Health and Wellbeing website.