Applied Harmonic Analysis

Math 658-600 -- Fall 2008

Instructor: Dr. Francis J. Narcowich
Office: 302 Milner Hall
E-mail: fnarc@math.tamu.edu
Phone: 845-7369
URL: /~francis.narcowich/
Office Hours: MWF 10-11, and by appointment.

Catalogue Description: Applied Harmonic Analysis. (3-0). Credit 3. Fourier series and Fourier Transform; discrete (fast) Fourier transform; discrete cosine transform; local cosine transform; Radon transform; filters; harmonic analysis on the sphere; radial, periodic, and spherical basis functions; applications. Prerequisite: MATH 304, MATH 308.

Text: Fourier Analysis and Its Applications, 1st Edition, by Gerald B. Folland.

Time & Place: MWF 1:50-2:40, ZACH 322.

Topics: From the text, we will cover in detail chapter 2 (Fourier series), chapter 7 (Fourier transforms), and chapter 9 on distributions, along with sections from chapter 6 on orthogonal polynomials. Applications here include signal analysis - sampling theorem, fast Fourier transform (FFT), filters, and the uncertainty principle, and others. In addition to the topics mentioned above, we will also cover these: wavelets (signal processing, compression), Radon transform (CAT scan), harmonic analysis on the sphere (geophysics, atmospheric science, physics, etc.), radial basis functions (neural networks, scattered-data surface fitting). Notes will be provided for these topics.

Grading. Your grade will be based on homework (25%), two in-class tests (25% each), and a presentation of a special topic (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 as soon as possible.

Academic Integrity

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."

Aggie Honor Code:   "An Aggie does not lie, cheat, or steal or tolerate those who do."

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Updated 8/22/08 (fjn).