Fourier Series & Wavelets

Math 414 - Spring 2001

Instructor: Dr. Francis J. Narcowich
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: 845-7369
URL: /~francis.narcowich/
Office Hours, TBA - and by appointment

Catalogue Description: MATH 414. Fourier Series & Wavelets. Fourier series and wavelets with applications to data compression and signal processing. Prerequisite: MATH 222 or MATH 304 or MATH 311

Required Text: A. Boggess and F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice-Hall, in press. Available from the MSC bookstore.

Programming language: Some computer programming experience would be very helpful. The choice of programming language is not important. In class, we will use MATLAB.

Syllabus
Inner products spaces and Fourier series (4 weeks; chapters 0 & 1)
Fourier transform (2 weeks; chapter 2)
Discrete Fourier analysis (1 week; chapter 3)
Haar wavelet (1.5 weeks; chapter 4)
Multiresolution analysis (2.5 weeks; chapter 5)
Daubechies wavelets (2 weeks; chapter 6)
Other wavelet topics (1 week; chapter 7)

Grading System & Tests: Your grade will be based on a project (due 1 May), homework, a mid-term (6 March), and a final exam (4 May, 3-5 pm). The project will count for 20% of your grade, homework for 40%, the mid-term for 20%, and the final for 20%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, contact me as soon as possible.

Copying Course Materials: ``All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.''

Homework and Projects: You may consult with each other on homework problem sets, BUT only submit work which is in your own words AND cite any sources of help (web, texts or people). Late homework will not be accepted. The project will be due on 1 May. You may work in small groups (at most 3), but again state clearly the contributions of each member of the group.