Applied Harmonic Analysis

Math 658-600 – Fall 2012

Instructor: Dr. Francis J. Narcowich: Office: 302 Milner Hall; E-mail: fnarc@math.tamu.edu; Phone: (979) 845-7554 (Messages only.); URL: /~francis.narcowich/; Office Hours: MWF 11:30-12:30, 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. (In addition, you will definitely need to understand analysis at the level of Math 447.)

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

Time & Place: MWF 10:20-11:10, CE 222.

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

Grading System & Tests: Your grade will be based a midterm, a final exam (Tuesday, December 11, 8-10 pm), and homework. The mid-term will count for 35% of your grade, the homework for 30%, and the final examination will count for the remaining 35%. 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."

Americans with Disabilities Act Policy Statement: "The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe that you have a disability requiring an accommodation, please contact the Department of Student Life, Services for Students with Disabilities, in Room 126 of the Koldus Building or call 845-1637."

Updated 8/26/2012 (fjn).