ECE 301 Signals and Systems

Lecture Hours: 3. Credits: 3.

Normally Offered: Each Fall, Spring

Prerequisites: ECE 202

Prerequisites by Topic: an understanding of basic concepts of linear circuits as examples of linear systems; an understanding of the application of unilateral Laplace transforms to circuit problems; a familiarity with the solution of linear constant coefficient differential equations; a familiarity with complex numbers and calculus, including power series.

Corequisites: None.

Catalog Description: Classification, analysis and design of systems in both the time- and frequency-domains. Continuous-time linear systems: Fourier Series, Fourier Transform, bilateral Laplace Transform. Discrete-time linear systems: difference equations, Discrete-Time Fourier Transform, bilateral z-Transform. Sampling, quantization, and discrete-time processing of continuous-time signals. Discrete-time nonlinear systems: median-type filters, threshold decomposition. System design examples such as the compact disc player and AM radio.

Course Objective(s): To develop the analytical tools and techniques needed for the design and analysis of discrete-time and continuous-time linear systems - convolution, transforms, and sampling theory are therefore the primary topics.

Required Text(s):

1. Signals and Systems, 2nd Edition, Oppenheim, Willsky, & Young, Prentice-Hall, 1997, ISBN No. 0-13-814757-4.

Recommended Reference(s):

1. MatLab: Student Version, Current Edition, The MathWorks, Inc..

Course Outcomes:

A student who successfully fulfills the course requirements will have demonstrated:

1. an ability to classify signals (e.g. periodic, even) and systems (e.g. causal, linear) and an understanding of the difference between discrete and continuous time signals and systems. [1,2;a]
2. an ability to determine the the impulse response of a differential or difference equation. [1,2;a]
3. an ability to determine the response of linear systems to any input signal by convolution in the time domain. [1,2,4;a,e,k]
4. an understanding of the definitions and basic properties ( e.g. time-shift, modulation, Parseval's Theorem) of Fourier series, Fourier transforms, bilateral Laplace transforms, Z transforms, and discrete time Fourier transforms and an ability to compute the transforms and inverse transforms of basic examples using methods such as partial fraction expansions. [1,2;a]
5. an ability to determine the response of linear systems to any input signal by transformation to the frequency domain, multiplication, and inverse transformation to the time domain. [1,2,4;a,e,k]
6. an ability to apply the Sampling theorem, reconstruction, aliasing, and Nyquist's theorem to represent continuous-time signals in discrete time so that they can be processed by digital computers. [1,2,4;a,e,k]

Lecture Outline:

Lectures	Topic(s)
3	Systems design tasks and tool, system classifications
6	Time-domain solution of difference equations
5	Discrete-time impulse responses and convolution
4	Sums of sinusoids and the Fourier Series
5	The Fourier Transform and its properties, transfer functions
3	Sampling and quantization
4	Discrete-Time Fourier Transform and its properties
2	Discrete-time processing of continuous-time signals
5	The bilateral z-Transform and its properties
3	The bilateral Laplace Transform and its properties
2	System design examples
3	Tests