Fourier Series & Wavelets

Math 414-501 — Spring 2018

Instructor: Dr. Francis J. Narcowich
Office: 611D Blocker
E-mail: fnarc@math.tamu.edu
Phone: 979-845-7554 (Messages only.)
URL: http://www.math.tamu.edu/~francis.narcowich/
Office Hours: MWF 11:10-12, TR 10:30-11:30, and by appointment.

Catalogue Description: MATH 414. Fourier Series & Wavelets. Fourier series and wavelets with applications to data compression and signal processing. Prerequisite: MATH 323 or MATH 304 or MATH 311

Required Text: A First Course in Wavelets and Fourier Analysis, 2nd Edition, by Boggess & Narcowich

Time & Place: MWF 10:20-11:10 pm, BLOC 117

Programming language: Experience with MATLAB would be very helpful.

Grading System & Tests: Your grade will be based on a project, homework, and three in-class tests ( February 19, March 21 and April 27 ).The project will count for 20% of your grade, homework for 20%, and each in-class test 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). Be aware that usually only some of the problems from an assignment will be graded. Late homework will not be accepted. Information concerning projects may be found on at this webpage: Project Information.

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 you have a disability requiring an accommodation, please contact Disability Services, currently located in the Disability Services building at the Student Services at White Creek complex on west campus or call 979-845-1637. For additional information, visit the Department of Disability Services.

Schedule

Week Section Topic
1
1.1.3, 1.2.1-1.2.3 Fourier series (FS): motivation, calculation, examples
2
1.2.1-1.2.3 FS eamples, function extensions, symmetry, Fourier cosine/sine series (FCS/FSS), examples
3
1.2.4-1.2.5, 1.3,1-1.3.2 Pointwise onvergence — definition and examples, complex form of FS, Fourier kernel —; partial sums (simplified version)
4
1.3.1-1.3.3 Riemann-Lebesgue lemma, proof of pointwise convergence of a Fourier series, uniform covergence — definition and examples
5
0.5, 1.3.4-1.3.5. inner products, orthogonal bases, Parseval's equation, convergence in the mean — defintion examples, chapter 1 review
6
Test 1 (2/19/18), 2.1.1-2.1.2 Test 1 (covers Chapter 1), Fourier transform (FT), examples
7
2.2.1, 2.2.2, 2.3 Properties of the FT, convolution theorem, filters
8
2.3.1, 2.3.3, 2.4 3.1 Time-invariant filters, causal filters, sampling theorem
3/12 - 3/16/18 N/A Spring Break
9
Test 2 (3/21/18), 3.1 Review, catch up, Test 2 (covers Chapter 2), discrete Fourier transform
10
3.1.1-3.1.4, 3.2.1, Good Friday/Reading day (3/30/2018) Discrete Fourier transform, fast Fourier transform (FFT), applications, discrete signals & filters
11
4.1, 4.2, 4.3 Haar wavelets, decomposition and reconstruction algorithms, filter representation
12
5.1, 5.2 Multiresolution analysis (MRA), examples, scaling relation & scaling function, wavelet & wavelet spaces
13
5.3.3, Theorem 5.2.3, 6.2-6.3 Decomposition and reconstruction algorithms, connection with FT, and existence criteria for wavelets, Daubechies wavelets
14
Test 3 (4/27/18) Review, catch up, Test 3 (covers Chapter 4, 5.1, 5.2, 5.3.3-5.3.4, 6.2)
15
6.2 presentations
Tuesday, 5/8/18 N/A Projects due at noon

Updated 1/28/2018.