San Francisco State University
Math 471
Fall, 2015
Introduction to Fourier and Wavelet Analysis

Instructor: Dr. Shidong Li
Office: TH 929,    Phone: x81481,  email: shidong@sfsu.edu
Office Hours:  T, T 13:00 - 14:00, or by appointment.
Prerequisite:  C or better in Math 370.

Text: An Introduction to Wavelet Analysis, by David Walnut.

Fourier analysis is perhaps the most widely used mathematics in practical applications. From classical radio, modern internet data communications to micro chips used in cell phones and computers, Fourier Transform is (still) one of the most important components. Understanding Fourier Transform is rewarding in every aspects of one's career and/or intellectual life. Wavelet transform is something fairly new, having already a great deal of applications in modern telecommunication and data/image compressions and transmissions. The two are connected, yet quite different. The combination of the two subjects in one class will give you a good perspective of the two techniques widely seen in practical life, as well as in mathematical research.

Topics to be covered:
Convergence of sequences and series of functions.
Fourier Series of periodic functions, and the convergence theorems.
Fourier Intergral/Transform, convolution, inversion, plancherel's formula, and some applications.
Wavelets, basics of what, why and how; Multiresolution Analysis.
Frames, basics and usefulness.

Homework are assigned on each lecture.  Students are expected to spend 3-5 hours on each assignment.