Signal and
Systems I
This is an introductory course of signals and
systems. The most important properties of continuous-time and discrete-time
signals and systems are considered: periodicity, linearity, time-invariance,
causality, impulse response, convolution representation. Their analysis in the
frequency domain is presented by means of the Fourier Transform and the
Discrete-Time Fourier Transform (DTFT).
ENGR 203, MTH 256
Benoit Boulet, Fundamentals of Signals
and Systems, Course Technology, 2005. ISBN
9781584503811
Recommended MATLAB Text: W. Palm, Introduction to MATLAB 7 for
Engineers, McGraw-Hill, 2006. ISBN 0-07-2548185
|
Midterm 1 |
25% |
|
Midterm 2 |
30% |
|
Final |
35%
|
|
Homework |
10%
|
There will be a weekly micro pop quizzes. These quizzes will be counted as extra credits which can be up to 10% total.
Chapter 1 -
Elementary Continuous-Time and Discrete Time Signals and Systems
o
Functions of Time as Signals
o
Transformations of the Time Variable
o
Periodic Signals
o
Exponential Signals
o
Periodic Complex Exponential and Sinusoidal Signals
o
Finite-Energy and Finite-Power Signals
o
Even and Odd Signals
o
Discrete Time Impulse and Step Signals
Chapter 2-
Linear Time-Invariant Systems
o
Discrete-Time LTI Systems: The Convolution Sum
o
Continuous-Time LTI Systems: The Convolution Integral
o
Properties of Linear Time-Invariant Systems
Chapter 3 - Differential and Difference LTI Systems
o
Causal LTI Systems Described by Differential Equations
o
Causal LTI Systems Described by Difference Equations
o
Characteristic Polynomials and Stability of Differential and Difference Systems
o
Differential System
o
Eigenfunctions of LTI Difference and Differential Systems
Chapter 4 -
Fourier Series Representation of Periodic Continuous-Time Signals
o
Linear Combinations of Harmonically Related Complex Exponentials
o
Determination of the Fourier Series Representation of a Continous-Time Periodic Signal
o
Graph of the Fourier Series Coefficients: The Line Spectrum
o
Fourier Series of a Periodic Rectangular Wave
o
Gibbs Phenomenon
o
Fourier Series of a Periodic Train of Impulses
Chapter 5 -
The Continuous-Time Fourier Transform
o
Fourier Transform as the Limit of a Fourier Series
o
Properties of the Fourier Transform
o
Examples of the Fourier Transform
o
The Inverse Fourier Transform
o
Duality
o
Convergence of the Fourier Transform
o
The Convolution Property in the Analysis of LTI Systems
o
Fourier Transforms of Periodic Signals
Chapter 12 -
Discrete-Time Fourier Series and Fourier Transform
o
Response of Discrete-Time LTI Systems to Complex Exponentials
o
Fourier Series Representation of Discrete-Time Periodic Signals
o
Properties of the Discrete-Time Fourier Series
o
Discrete-Time Fourier Transform
o
Properties of the Discrete-Time Fourier Transform
o
DTFT of Periodic Signals and Step Signals
o
Duality
A.V. Oppenheim and
A.S. Willsky, Signals and Systems,
Second Edition, Prentice Hall, 1997, ISBN 0-13-814757-4
C.L. Phillips and J.M. Parr, Signal,
System, and Transforms, Second Edition, Prentice Hall, 1991, ISBN
0-20-109589-0
D.K. Lindner, Introduction to Signals and
Systems, First Edition, McGraw Hill, 1999, ISBN
Fourier transform