| Instructor(s) | Dr. Dafna Sussman [Coordinator] Office: ENG317 Phone: (416) 979-5000 x 553767 Email: dafna.sussman@torontomu.ca Office Hours: Monday 12-1pm By appointment | ||||||||||||||
| Calendar Description | This 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. | ||||||||||||||
| Prerequisites | EES 604, CEN 199 | ||||||||||||||
| Antirequisites | ELE 532 | ||||||||||||||
| Corerequisites | None | ||||||||||||||
| Compulsory Text(s): |
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| Reference Text(s): |
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| Learning Objectives (Indicators) | At the end of this course, the successful student will be able to:
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 | ||||||||||||||
| Teaching Assistants | TBA | ||||||||||||||
| Course Evaluation |
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 4, 9, and 13, approximately 20-30 minutes, during the last 30min of the lab. - Midterm Exam is in Week 8, two and half hours, problem-solving, during the regular lecture hours (covers Weeks 1-7 of lecture notes). - Final Exam is scheduled during the undergraduate exam period (covers all course material with emphasis on the material not covered on the midterm). | ||||||||||||||
| Other Evaluation Information | - 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. | ||||||||||||||
| Other Information | None | ||||||||||||||
Week | Hours | Chapters / | Topic, description |
|---|---|---|---|
1 & 2 | 6 | 1.1-1.4, 2.1-2.7 | This course introduces fundamental concepts in signal processing, starting with the basic definition and characteristics of signals. The size of a signal is quantified by its energy and power, which helps classify it. We can also manipulate signals using operations like time-shifting, time scaling, and time reversal. Signals can be classified into different categories, such as continuous-time vs. discrete-time, and periodic vs. aperiodic. Other classifications include causal, non-causal, and anti-causal signals. The course also introduces useful signal models, including the unit step function, unit impulse function, and exponential functions, which serve as building blocks for more complex signal analysis. |
3-5 | 9 | 2.8-2.15, 3.1-3.7 | Time-domain analysis of continuous-time systems involves several key concepts. The zero-input response is the system's output due to its initial internal conditions, while the zero-state response is the system's output to external inputs. The total system response is the sum of these two. The convolution integral is a fundamental tool used to find the zero-state response, and it relies on the system's unique unit impulse response, which is its output when the input is a unit impulse. The analysis of linear time-invariant (LTI) systems is a core focus because their properties of linearity and time-invariance simplify calculations and predictions. Finally, the course also addresses system stability, distinguishing between internal (asymptotic) stability and BIBO (bounded-input bounded-output) stability and exploring the important relationships between them. |
6 & 7 | 6 | 3.8-3.14, 9.1-9.4 | 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. |
8 | 3 | Midterm Exam | |
9 & 10 | 6 | 11.1-11.13, 12.1-12.10 | The Fourier transform is a powerful tool for analyzing aperiodic signals, which are represented by the Fourier integral. This analysis involves understanding the Fourier transforms of some useful functions and the key properties of the Fourier transform. The Fourier transform is also used to study signal transmission through LTIC systems and to design ideal and practical filters. A signal's energy can be determined in the frequency domain using the Fourier transform, which has important applications in communications. |
11 | 3 | 10.1-10.4 | Applications of Fourier transform properties, including how they are used to analyze signals and design systems like bandpass filters, which selectively allow a certain range of frequencies to pass through. The module also introduces the Laplace transform, which extends the Fourier transform's capabilities to a broader class of signals. A key concept for the Laplace transform is the Region of Convergence (ROC), which defines the set of complex numbers for which the transform integral exists and converges. |
12 & 13 | 6 | 13.1-13.4 | 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. |
Week | L/T/A | Description |
|---|---|---|
2 | T | Tutorial 1: Introduction to MATLAB |
3 & 4 | L | Lab 1: Signals and Systems Representation |
5 & 6 | L | Lab 2: Time-Domain Analysis of CT Systems |
7 / 8 (Monday section) | T | Tutorial 2: Midterm Review Examples |
9 & 10 | L | Lab 3: The Fourier Series |
11 & 12 | L | Lab 4: The Fourier Transform |
13 | T | Tutorial 3: Final Exam Review Examples |
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