**Instructor: J. D. Ward****Office:**305 Milner Hall**E-mail:**`jward@math.tamu.edu`**Phone:**845-7554 (math dept.)**URL:**`http://www.math.tamu.edu/~joe.ward/`**Office Hours**: MW 3:30-4:45 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*:

**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 (** Thurs. February 21** &
**Thurs. March 28**) and a final exam (** Wednesday, May 8, 1:00-3:00**). 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 4**). 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

- assignment 1 (Due Thurs. Jan. 24): 3, 4, 7, 10 (ch. 1, p. 83)
- assignment 2 (Due Thurs. Feb. 7): 9, 21, 26, 28, 36 (ch. 1, p. 83): 22, 30, 32, 33, 34 (Matlab)
- Exam I(Thurs. Feb. 21): material stops at linear filters p. 110: Be able to compute Fourier series, Fourier transforms and convolution
- (continued):Know Parseval and Plancherel and to compute nearest L_2 points; know properties of Fourier transform
- assignment 3 (Due Tues.. Feb. 26): (ch. 2, p. 127): 2, 4, 5, 6
- assignment 4 (Due Thurs. March 7): (ch. 2, p. 127): 8, 9, 13, 14
- Assignment 5 (Due Thurs. March 21) Ch.3, p. 156: 7, 8, 9, 13, 14, 15
- Assignment 6 (Due TUES. April 16) Ch.4, p. 186: 1,2,3,4,5,6,7,9
- Assignment 7 (Due the same day of the final exam) Ch.5, p. 230: 2, 3, 4, 5, 6, 8a-d, 9, 12, 13
- PRESENTATIONS: THURS. APRIL 25 MILNER 317; 1:30 -- 4:00