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 311Required Text: A First Course in Wavelets and Fourier Analysis, 2nd Edition, by Boggess & Narcowich
Time & Place: MWF 12:40-1:30 pm, BLOC 164
Programming language: Experience with MATLAB would be very helpful.
Grading System & Tests: Your grade will be based on a project, homework, two in-class tests ( Wednesday, February 26 & Wednesday, April 8). and an online final exam (Friday, May 1). The project will count for 20% of your grade, homework for 20%, each in-class test for 20%, and the final exam 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
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. Texas A&M University is committed to providing equitable access to learning opportunities for all students. If you experience barriers to your education due to a disability or think you may have a disability, please contact Disability Resources in the Student Services Building or at (979) 845-1637 or visit the Department of Disability Services. Disabilities may include, but are not limited to attentional, learning, mental health, sensory, physical, or chronic health conditions. All students are encouraged to discuss their disability related needs with Disability Resources and their instructors as soon as possible.
Revised Schedule
| Week | Section | Topic |
|---|---|---|
| |
0.1-0.3 | Introduction, inner product spaces |
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0.4-0.5 | 1/20/20, Martin Luther King, Jr. Day, Holiday; inequalities, orthogonality, projections |
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0.5.2, 0.5.3, 1.2.1 | Least squares, projections, orthogonality relations for Fourier series (FS) |
| |
1.2.1-1.2.5 | FS examples, Fourier sine/cosine (FSS,FCS), complex form of FS |
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1.3.1-1.3.4 (simplified version) | Fourier kernel, Riemann-Lebesgue lemma, proof of pointwise, uniform convergence of an FS, examples |
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1.3.4, 1.3.5 | Uniform convergence, Parseval's equation, convergence in the mean |
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Test 1 (2/26/20), 2.1 | Review, Test 1; Fourier transform, examples |
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2.2, 2.3.1 | Properties of the FT, convolution theorem, linear time-invariant filters |
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N/A | Spring Break, extended |
| 3.1.1-3.1.4, 3.2.1 | | |
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2.3.1, 2.3.2, 4.1 | LTI filters, causal filters, wavelets |
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4.2, 4.3.1, 4.3.2 | Haar approximation and wavelet spaces, decomposition and reconstruction algorithms |
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Test 2 (4/8/20) | Review, Test 2; Good Friday, April 10, reading day. |
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3.3.1, 4.3.3, 4.4, 5.1.1 | Discrete signals and filters, filter diagrams, processing a signal, MRA, Haar MRA and Shannon MRA |
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5.2.2-5.2.3, 5.3.3, 6.1, 6.2 | Decomposition and reconstruction algorithms, connection with FT, and existence criteria for wavelets, Daubechies wavelets |
| |
6.2, 6.3 | Classification of Daubechies' wavelets, data extensions, review; |
| Friday, 5/1/2020 | N/A | Final exam (online), 10:30-12:30 |
| Tuesday, 5/5/2020 | N/A | Projects (online), due at 12 noon |
Updated 4/17/2020.