Instructor: J. D. Ward

Office: 305 Milner Hall

E-mail: jward@math.tamu.edu

Phone: 845-1169

URL: http://www.math.tamu.edu/~joe.ward/

Office Hours: WF 3:30-5:00 or 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: purchase at Copy Corner:694-2679(across from Target in C.S.)

Programming language: Experience with MATLAB would be helpful.

Syllabus

Inner product 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, homework, two in-class tests ( February 25 & April 8) and a final exam ( May 11, 8:00-10:00). The project will count for 20% of your grade, homework for 20%, each in-class test 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.

Homework and Projects: 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). Late homework will not be accepted. The project will be due at the end of the semester (May 12). 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. In addition to a written version of the project, each group will make a brief oral report to the class.

Americans with Disabilities Act

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 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.

Academic Integrity Statement

Honor Council Rules and Procedures

• p. 96-101--- 3, 4, 9, 10, 11
• p. 96-101--- 16, 17, 22, 24, 32 (due Fri. Feb. 6)
• p. 96-101--- 18, 26, 28, 29, 30 (Matlab needed) (due Fri. Feb. 20)
• p. 140------ 2, 4, 5, 6, 10 (due Fri. Feb. 20)
• p. 140------ 13, 14 (due Fri. March 6)
• p. 150------ prove last two "bullets" of Thm 3.4 (due Fri. March 27)
• p. 166------ 7, 8, 9, 11, 13, 14, 15 (due Fri. March 27)
• p. 194------ 1, 2, 3, 4, 9 + problem given in class (due April 10)
• p. 194------ 6, 7, 10 (due April 10)
• p. 235------ 2, 3, 4, 5, 8(a-d), 12 (due April 24)
• p. 236------ 6, 7, 9, 10, 13, 17 (for final exam)
• p. 251------ 1 (w/o sketching), 2, 3 (for final exam)