Al Boggess. Office in Bloc 623. Tentative office hours are Monday - Thursday, 1:30 - 2:30 or by appointment. E-mail address is boggess@math.tamu.edu - - - URL address is http://www.math.tamu.edu/~boggess/
Fourier Series and Wavelets are important mathematical building blocks for signal analysis and many other areas in science and engineering. Fourier Series is the study of how a function (or signal) can be decomposed into a sum of sine and cosine waves of various frequencies. Wavelets are similar to sines and cosines in that they look like waves of various frequencies. However, they are different in that wavelets can be isolated by the user (unlike sine and cosine waves which keep repeating forever). This localization feature of wavelets allows the user to filter or modify certain parts of the signal without affecting other parts.
This course will present an overview of Fourier and Wavelet Analysis along with some applications. The goal of this course is to present the general ideas behind the construction of Fourier Series and Wavelets. The technical jargon of signal analysis and other fields of applications will be minimized. No prior knowledge of Fourier Series or Wavelets will be assumed. The prerequisites are a three semester calculus sequence and linear algebra (Math 304, 311 or 222). Some computer programming experience would be very helpful. The choice of programming language is not important.
The main reference for the course is a set of lecture notes entitled Fourier Analysis and Wavelets by Boggess and Narcowich and is on sale at University Copy Center (on College Main) and the price is about $15. Other references include the following.
Grades will be determined by problem sets, a midterm exam and a written project. The grade weights are as follows.
Problem Sets Midterm Project
50% 25% 25%
The midterm will be an in-class exam. You may consult with each other on homework problem sets, BUT only submit work which is in your own words AND be sure to cite any sources of help (either texts or people). The project will be due at the end of the semester. You may work in small groups (at most 3) but again a clear statement must be made that specifies the contributions of each member of the group.
Make-ups and late work will be allowed with a University authorized excuse in writing (see University Regulations).
All handouts and web documents for this course are protected by copyright. One copy may be made (our downloaded) for personal use. Multiple copies require permission of the instructor.