Course Outline (W2020)

ELE632: Signals and Systems II

Instructor(s)Javad Alirezaie [Coordinator]
Office: ENG452
Phone: (416) 979-5000 x 6092
Email: javad@ryerson.ca
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/tutorial per week for 12 weeks

Teaching AssistantsAleksander Banbur abanbur@ryerson.ca
 Randy Tan  randy.tan@ryerson.ca
 Farah Nassif fnassif@ryerson.ca
 Mahdi Shams mahdi.shamsi@ryerson.ca
 Garima Sharma garima.sharma@ryerson.ca
Course Evaluation
Midterm Exam 25 %
Quizzes 15 %
Final Exam 40 %
Lab Experiments 20 %
TOTAL:100 %

Note: In order for a student to pass a course with "Theory and Laboratory" components, in addition to earning a minimum overall course mark of 50%, 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 for details on the Theory and Laboratory components.

ExaminationsMidterm exam in Week 7, two hours, closed-book (covers Weeks 1-6).
 Final exam, during exam period, three hours, closed-book, formula sheet will be provided.
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 marks are based on attendance, successful completion of pre-lab problems, participation, completion of experiment steps and lab reports.  Students will have the responsibility to achieve a working knowledge of the software packages and the hardware systems that will be used in the lab.  Students will work in pairs.
Other InformationNone

Course Content



Chapters /

Topic, description



Chp 3 Sect 1-3

Introduction to discrete-time systems and signals.



Chp 3 Sect 3-4

Time domain analysis of discrete time systems useful discrete-time signals.



Chp 3 Sect 4-5

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



Chp 3 Sect 6-7

Unit impulse response system response BIBO stability criterion.



Chp 3 Sect 8-10

Convolution and its properties LTI systems and impulse response.



Chp 5 Sect 1-3

z-Transform properties inverse transform solution to difference equations.



Chp 5 Sect 3

z-Transform properties.  Midterm Exam.



Chp 5 Sect 4-6

z-Transform system realization frequency response of discrete systems pole-zero analysis stability.



Chp 5 Sect 7-9

Bilateral z-Transform. Discussion of regions-of-Convergence.



Chp 8 Sect 5-6

Spectral Sampling DFT properties and applications FFT.



Chp 9 Sect 1-2

Fourier analysis of discrete systems DTFS periodic and aperiodic signal representation.



Chp 9 Sect 3-4

Properties of DTFT system analysis using DTFT digital filters.



Chp 9 Sect 5-6

DTFT connection with CTFT DTFT and z-Transform. Review.

Laboratory/Tutorials/Activity Schedule






Experiment 0:  Introduction to MATLAB DSP toolbox



Experiment 1: Time-Domain Analysis of Discrete-Time Systems-Part 1



Experiment 2: Time-Domain Analysis of Discrete-Time Systems-Part 2



Experiment 3 Discrete-Time Fourier Series



Experiment 4: Discrete Time Fourier Transform



Experiment 5: Sampling and Discrete Fourier Transform

Policies & Important Information:

  1. Students are required to obtain and maintain a Ryerson e-mail account for timely communications between the instructor and the students;
  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. Refer to our Departmental FAQ page for information on common questions and issues at the following link: https://www.ee.ryerson.ca/guides/Student.Academic.FAQ.html.

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. Health certificates - If a student misses the deadline for submitting an assignment, or the date of an exam or other evaluation component for health reasons, they should notify their instructor as soon as possible, and submit a Ryerson Student Health Certificate AND an Academic Consideration Request form within 3 working days of the missed date. Both documents are available at https://www.ryerson.ca/senate/forms/medical.pdf.. If you are a full-time or part-time degree student, then you submit your forms to your own program department or school;
  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 www.ryerson.ca/senate/forms/relobservforminstr.pdf. 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 - www.ryerson.ca/studentlearningsupport/academic-accommodation-support) should provide their instructors with an Academic Accommodation letter that describes their academic accommodation plan.

Academic Integrity

Ryerson'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(https://www.ryerson.ca/senate/policies/pol60.pdf) and to the Academic Integrity Office website (https://www.ryerson.ca/academicintegrity/).

Important Resources Available at Ryerson

  1. The Library (https://library.ryerson.ca/) provides research workshops and individual assistance. Inquire at the Reference Desk on the second floor of the library, or go to library.ryerson.ca/guides/workshops
  2. Student Learning Support(https://www.ryerson.ca/studentlearningsupport) offers group-based and individual help with writing, math, study skills and transition support, and other issues.