# Course Outline (F2019)

## BME532: Signals And Systems I

Instructor(s)Dafna Sussman [Coordinator]
Office: ENG317
Phone: (416) 979-5000 x 3767
Email: dafna.sussman@ryerson.ca
Office Hours: Fridays 9:30-10:30am (limited to 10min per student, by appointment)
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.
PrerequisitesEES 604, CEN 199
AntirequisitesELE 532
Corerequisites

None

Compulsory Text(s):
1. Linear Systems and Signals, by B.P. Lathi, third edition 2018. ISBN: 0190200176.
Reference Text(s):
Learning Objectives (Indicators)

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

1. Learn important signal and system classifications for further processing. For example if a system is Linear and Time invariant, then output of the system to all inputs can be predicted using the impulse response and using convolution. (3a)
2. 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 result of evaluation to detect if a continuous-time system is Linear Time-Invariant (LTI). To discern additional criteria. In case the system is LTI, additional characteristic of the system (impulse response of the system) is calculated to facilitate calculation and evaluation of the system's output. (4b)
3. Select and perform strategies to generate information about continuous-time signals (properties such as power or energy finiteness) and systems (properties such as linearity, stability, causality) that may be used to modify, improve, or elaborate a design state. (4c)
4. Understanding system property and limitation, fundamental problems in sampling. Learning the role of important signals such as sinc and delta and role of them in system design and analysis. (5a)
5. 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)
6. Illustrate concepts of continuous-time signals and systems through graphical presentation of their properties. (7c)
7. Finding relationship between signals, building a signal based on other existing basis, 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/tutorial per week for 12 weeks

Teaching AssistantsBinh Nguyen (binh.nguyen@ryerson.ca)
Karl Magtibay (karl.magtibay@ryerson.ca)
Matthew Basso (mnbasso@ryerson.ca)
Course Evaluation
 Quizes ( 3 x 5%) 15 % Lab 1 (in pairs) 3 % Lab 2 (in pairs) 4 % Lab 3 (in pairs) 4 % Lab 4 (in pairs) 4 % Midterm Test 30 % Final Exam 40 % 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 9, two hours, problem solving, closed book (covers Weeks 1-8).
Final exam, during exam period, three hours, closed-book (covers Weeks 1-13 with emphasis
on Weeks 9-13).
Other Evaluation InformationThere are assigned problems for each chapter posted on the course D2L. The assignment will not be collected. However, students are expected to solve all problems in preparation for the quizzes and exams.

Lab marks are based on attendance, successful completion of pre-lab problems, participation, completion of experiment steps, lab reports and successful reply to your TA questions during submission. 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.
Other InformationNone

### Course Content

Week

Hours

Chapters /
Section

Topic, description

1-3

9

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)

4-6

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 responseâ€“the method of undetermined coefficients, system stability: internal (asymptotic) stability, BIBO stability, criterion relationship between BIBO and asymptotic stability, intuitive insights into system behaviour.
(Reference: Chapter 2 Sections 2.1-2.6 and 2.8-2.9)

7-9

3

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)

9-11

9

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)

11-12

5

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

12-13

7

The Laplace Transform
The Laplace transform, 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, frequency response of an LTIC system.
(Reference: Chapter 4 Sections 4.1-4.2 4.4 and 4.6)

### Laboratory/Tutorials/Activity Schedule

Week

Lab

Description

2

0

Matlab Introduction Tutorial (2hrs)
It is very important to attend the Matlab tutorial scheduled for Week 2 and inform your TA of your lab partner.
(Reference Tutorial Note)

3-4

1

Signals and Systems Representations (4hrs)
In this experiment you will work with simple Matlab functions and will explore some signal properties.
(Reference Chapter 1)

5-7

2

Time-Domain Analysis of Continuous-Time Systems (4hrs)
In this experiment you will learn how to use M-files in Matlab and exercise convolution and system properties.
(Reference Chapter 2)

8-9

3

The Fourier Series (4hrs)
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.
(Reference Chapter 6)

10-12

4

The Fourier Transform (4hrs)
In this experiment you will investigate properties of the Fourier transform.
(Reference Chapter 7)

### 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.

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