WAVELET ANALYSIS

Math 668--Fall 1998

Instructor: Dr. Francis J. Narcowich
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: 845-7369
URL: /~francis.narcowich/
Office Hours, TR 9:15-10:45; and by appointment.

Catalog Description: Time-frequency analysis, integral wavelet transform, multiresolutional analysis, dyadic wavelets and inversions, frames, classification of wavelets, dual basis and a duality principle, wavelet decompositions and reconstructions, spline wavelets, zero-crossings of spline-wavelet series, wavelet packets, multivariate wavelets. Prerequisite: MATH 304, MATH 409, MATH 417 or equivalents.

Required Text
S. Mallat, A Wavelet Tour of Signal Processing, Academic Press, San Diego, 1998.
Supplementary Materials
Wavelets
Fourier series & transforms
Notes
MATLAB
M-files
Chapters and sections to be covered
Chapter 1---overview
Chapter 2---Fourier transforms
Chapter 3---discrete transforms
Chapter 7---orthogonal/biorthogonal wavelets; 7.1-7.4, 7.7
Chapter 5---frames; 5.1--5.5
Chapter 8---wavelet packets, discrete cosine transform; 8.1-8.2
Chapter 4---time/frequency decompositions; 4.1--4.4
Chapter 11---signal compression; 11.1--11.2
Chapter 9---approximations; 9.1--9.3
Chapter 6---local singularities, edges, ``zoom''; 6.1--6.3
Visualization & computational aids---Matlab & Matlab Wavelet Toolbox

Tests

Grading: Your grade will be based on homework, two in-class tests, and a project or a final exam. The homework, each in-class test, and the project (or final) will count for 25%. 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 immediately.

Copyrights: The handouts used in this course are copyrighted. By "handouts," I mean all materials generated for this class, which include but are not limited to syllabi, quizzes, exams, lab problems, in-class materials, review sheets, and additional problem sets. Because these materials are copyrighted you do not have the right to copy the handouts, unless I expressly grant permission.