SIGNAL and SYSTEMS
ELEC ENG 3TP4
CALENDAR:
Time and frequency domain descriptions of
continuous-time and discrete-time signals
and linear systems,
including convolution, Fourier transforms, impulse response and frequency
response; Applications to control and communication systems.
Three lectures, one tutorial, one lab (every other
week); first term
Prerequisite: ELEC ENG 2CJ4 or 2DA3
Corequisite: MATH 3KO3
Antirequisite: ELEC ENG 3AA3
COURSE OBJECTIVES:
To discover the fundamental principles of representing signals and
linear systems
in the time and frequency domains, and to use these principles in the
analysis and design of linear control and communication systems.
COURSE LOADING:
-
Lectures: 3 1-hour lectures per week
-
Tutorial: 1 1-hour tutorial per week
-
Lab: 1 3 hour session every other week
-
Prelab preparation and assignments: 1.5 hrs per week
-
Study time: 4 hours per week
- Total hours per week: 11
CEAB WEIGHTING:
-
ES = 80%, D = 10%, M = 10%
TEXTBOOK:
-
S. Haykin and B. Van Veen, "Signals and Systems", J. Wiley
and Sons, 1999
DETAILED COURSE CONTENT:
Introduction (1 hour)
-
What are signals and systems? Examples from
control and robotics, communications, remote sensing,
biomedical, audio-visual entertainment.
Elementary Signals and Basic Operations (2 hours)
- Continuous-time and discrete-time; Periodic and non-periodic
- Shifting and scaling
- Sinusoidal signals; Complex exponentials; Impulse functions
- Block diagrams
- System properties: Stability, memory,
causality, invertibility, time invariance, linearity
Time Domain Representations of Linear Time-Invariant Systems (6 hours)
- Convolution discrete-time and continuous-time; impulse response;
- Stability and causality;
- Frequency response;
- Differential and difference equations;
Fourier Representations of Signals (5 hours)
-
Definitions:
Discrete-time Fourier Series, Fourier Series,
Discrete-time Fourier Transform, Fourier Transform,
-
Properties: Symmetries, time-shift properties, convolution,
modulation, Parseval, duality, time-bandwidth product
Applications of Fourier Representations (4 hours)
- Frequency response revisited, including differential/difference
equations
-
Relationships between Fourier representations;
- Basic concepts of filtering and filter design; Decibel measures
- Case Study: A simplified DSB-SC transmission system
- Sampling and ideal reconstruction of continuous-time signals;
practical reconstruction;
- Approximating the Fourier Transform using a Discrete-time
Fourier Series of the sampled signal;
Laplace Transform (4 hours)
- Review of Laplace Transform: Definition, properties,
poles and zeros
-
Region of convergence, inversion;
- Application to systems analysis: Causality, stability, system inversion,
-
Relationships to differential equations
and Fourier Transforms;
-
Fourier Transform from poles and zeros; Time domain response
from poles and zeros.
z-Transform (4 hours)
- Complementary treatment to that for the Laplace transform
Applications to Feedback Systems (9 hours)
-
Basic concepts of feedback
- Open and closed loop control
- Review of transient response of first and second-order systems;
Reduced-order models
- Stability: Root Locus; Nyquist Criterion;
Bode Diagram;
- Relative stability: Gain and phase margins; Damping ratio
- Simple control system design; Proportional, integral,
derivative,
phase lag, phase lead
Epilogue (1 hour)
- Characteristics of physical signals
- Characteristics of physical systems:
Time-variation; Non-linearities;
(Total Course = 36 hours)
LABORATORIES:
-
Lab 1: Representation of signals and systems in Matlab
-
Lab 2: Convolution: Impulse response, step response,
frequency response. (Matlab)
-
Lab 3: Filtering a periodic signal: Matlab performance
prediction and hardware measurement.
-
Lab 4: Stick Balancing: An application of
proportional-plus-derivative
control. (Matlab)
-
Lab 5: Design of a lag compensator.