ECSE-303 Signals and Systems
I
Fall 2005
Electrical and Computer Engineering
Instructor: Prof. Benoit Boulet
boulet@cim.mcgill.ca
www.cim.mcgill.ca/~boulet
McConnell Building, room 509
Course Outline
1. Elementary Continuous-Time
and Discrete-Time Signals and Systems (4 hours)
- Mathematical
functions as signal models
- Periodic
signals, exponential and sinusoidal signals
- Finite-energy
and finite-power signals
- Discrete-time
unit impulse and step functions
- Generalized
functions: derivatives and integrals of continuous-time unit step
functions
- Input-output
systems models
- Basic
system properties: linearity, memory, causality, stability, invertibility,
time-invariance
2. Linear Time-Invariant
(LTI) Systems (4 hours)
- Superposition
property of linear systems
- Discrete-time
LTI systems, the convolution sum
- Continuous
LTI systems, the convolution integral
- Properties
of LTI systems in terms of convolution representation
3. Differential
and Difference LTI Systems (3 hours)
- Definition,
role of initial conditions
- Impulse
response, forced response
- Characteristic
polynomial, natural frequency, stability
4. Fourier Representation
of Periodic, Continuous-Time Signals (3 hours)
- Eigenfunctions
and eigenvalues of LTI systems
- Definition
and properties of Fourier series
- Pointwise
and mean-square convergence of the Fourier series
- Representation
of discontinuous signals, Gibbs phenomenon
- Parseval
relation and representation of power signals
- Steady-state
response of LTI systems to periodic input signals
5. The Continuous-Time
Fourier Transform (5 hours)
- Representation
of the Fourier transform of an aperiodic signal as the limiting form
of a Fourier series representation of a periodic signal
- Definition
and properties of the continuous-time Fourier transform
- The
inverse Fourier transform, time-frequency duality, the uncertainty
principle
- The
convolution property and its application to the analysis of LTI systems
- Frequency
response of an LTI system
- Fourier
transform of generalized functions
- Ideal
low-pass, band-pass and high-pass filters
6. The Laplace
Transform ( 4 hours)
- Definition
of the two-sided Laplace transform and its relation to the continuous-time
Fourier transform
- Region
of convergence of the two-sided Laplace transform
- Inverse
Laplace transform and contour integration
- Properties
of the two-sided Laplace transform
- Definition
and properties of the one-sided Laplace transform
7. Application
of the Laplace Transform to LTI Differential Systems (3 hours)
- Impulse
response, convolution and the system function characterization of
continuous-time LTI systems
- LTI
differential systems, rational system functions, causality and stability
criteria
- Block
diagram representation
- Transient
and steady-state response of LTI differential systems
- Forced
and natural response of LTI differential system with nonzero initial
conditions
8. Time and
Frequency Analysis of BIBO stable, continuous-time LTI systems (5 hours)
- Relation
of poles and zeros of the system function to frequency response
- Bode
plots
- Frequency
response of first-order lag, lead, lead-lag and lag-lead systems
- Frequency
response of second-order systems: the peaking circle, maximal flatness,
high-Q (narrowband) approximation
- Step
response: rise time, overshoot, settling time, relative stability
- Response
of first and second-order systems: damping ratio, overdamped, underdamped,
and critically-damped systems
- Butterworth
filter design
- Ideal
delay systems, group delay, minimum phase and all-pass systems
9. Application
of Laplace Transform Techniques to Electric Circuit Analysis + Case Studies
(5 hours)
- KCL, KVL
and branch constitutive equations for LTI electric circuits
- Transform
circuit diagrams: analysis of transients and steady-state behavior
of LTI electric circuits with nonzero initial conditions
- Network
functions, relations to elements of nodal and loop matrices
- Case studies
in system analysis and design
11. Course Recap
(2 hours)
- Recapitulation
of course material to prepare for the final exam
Homework Assignments
There will be 6 homework assignments that,
taken together, will be worth 10% of your final grade
Midterm Tests
There will be 2 midterm tests (see course
schedule):
- MIDTERM
I, covering Chapters 1, 2, 3, worth 20% of your final grade
- MIDTERM
II, covering Chapters 4 and 5 worth 20% of your final grade
Final Exam
You will be responsible to review all material
covered in the course for the final exam. It will be worth 50% of your final
grade.
References
The textbook that we will use for this
course is the brand new Fundamentals of Signals and Systems, 1st
Ed. by B. Boulet, Da Vinci Engineering Press, Charles River Media, 2005,
ISBN 1584503815. It will be released on September 16 by the publisher. You
can pre-order it on Amazon (with a substantial pre-release rebate) which
should be the fastest way to get the book, or wait for it to arrive at the
bookstore around the end of September. Note that we will use this same textbook
in the course Signals and Systems II, so it is worth buying.
The reference textbook is Signals and
Systems, 2nd Ed. by Oppenheim, Willsky and Nawab, Prentice-Hall, 1997,
ISBN 0-13-814757-4.
Other suggested
references include:
- Signals
and Systems by Haykin and
Van Veen, John Wiley, 1999, ISBN 0-471-13820-7
- Fundamentals
of Signals and Systems Using MATLAB by Kamen and Heck, Prentice Hall, 1996, ISBN:
0-02-361942-2
- Signals
and Systems by Lindner, McGraw-Hill,
1999, ISBN 0-256-25259-9
Aug. 25, 2005
Benoit Boulet