EE 401: Transform Theory for Engineers
This is supplemental course information, designed to give you a fuller picture of the course and an expanded look at the topics covered. This is an unofficial document. The USC Course Catalog is the binding description of all university courses. Information such as books, materials covered, and the order of topics is subject to change. Please consult instructor for this semseter to get more upto date course information.
Catalog Data:
401 Transform Theory for Engineers (3, FaSp). Complex variables, Cauchy Riemann conditions, contour integration and residue theory; Fourier transform; Laplace transform; sampling theory. Discrete time filters, discrete and fast Fourier transform. Prerequisite: EE 301a and MATH 445.
Text book:
1. (Required) A. D. Poularikas and S. Seely, Signals and Systems, Second Edition (Krieger Publishing Co., Malabar, Florida, 1994)
2. (Supplemental) J. W. Brown and R. V. Churchill, Complex Variables and Applications, Sixth Edition (McGraw-Hill, New York, 1996)
Course Coordinators:
B. Keith Jenkins, Associate Professor of Electrical Engineering
Topics:
1. Complex variables, functions, and series; contour integration; analytic functions and uniqueness.
2. Continuous-time transforms, including general theory, Laplace and Fourier transforms.
3. Sampling and discrete-time transforms, including Z transform and some discrete variants of Fourier transform.
4. Mathematical foundation and tools, including the use of complex variables and integration in all topics of the course.
5. Application of transform techniques to solve problems.
Course Objectives:
To provide the student with a solid mathematical foundation in complex variables and common engineering transforms, including intuition in their use, and tools and techniques for applying them to a variety of problems.
Course Outcomes:
The students will be able to:
1. Determine over what domain a complex function is analytic by using a variety of tools.
2. Expand complex functions into power series, and assess region of convergence.
3. Evaluate contour integrals in the complex plane.
4. Understand the underlying representations of linear transforms, based on complete, orthogonal basis sets.
5. Perform forward and inverse Laplace transforms, with or without tables, by a variety of techniques.
6. Apply Laplace transform techniques to a variety of problems, including differential equations and system stability.
7. Understand and apply Fourier transform methods to one-dimensional and multi-dimensional problems.
8. Understand bandlimited functions, sampling, and aliasing.
9. Perform forward and inverse Z transforms, with or without tables, by a variety of techniques.
10. Apply Z transform techniques to a variety of problems, including difference equations and discrete-time system stability.
11. Understand the relationships between Laplace transform, Fourier transform, Z transform, and discrete Fourier transform.
12. Understand the relationships between various discrete versions of the Fourier transform.
Prepared by: B. Keith Jenkins Date: October 16, 2002
