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 10:2011:10 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 inclass tests ( February 19, March 21 and April 27 ).The project will count for 20% of your grade, homework for 20%, and each inclass test for 20%. Your letter grade will be assigned this way: 90100%, A; 8089%, B; 7079%, C; 6069%, D; 59% or less, F.
Makeup Policy: I will give makeups (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 antidiscrimination 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 9798451637. For additional information, visit the Department of Disability Services.
Schedule
Week  Section  Topic 


1.1.3, 1.2.11.2.3  Fourier series (FS): motivation, calculation, examples 

1.2.11.2.3  FS eamples, function extensions, symmetry, Fourier cosine/sine series (FCS/FSS), examples 

1.2.41.2.5, 1.3,11.3.2  Pointwise onvergence — definition and examples, complex form of FS, Fourier kernel —; partial sums (simplified version) 

1.3.11.3.3  RiemannLebesgue lemma, proof of pointwise convergence of a Fourier series, uniform covergence — definition and examples 

0.5, 1.3.41.3.5.  inner products, orthogonal bases, Parseval's equation, convergence in the mean — defintion examples, chapter 1 review 

Test 1 (2/19/18), 2.1.12.1.2  Test 1 (covers Chapter 1), Fourier transform (FT), examples 

2.2.1, 2.2.2, 2.3  Properties of the FT, convolution theorem, filters 
2.3.1, 2.3.3, 2.4 3.1  Timeinvariant filters, causal filters, sampling theorem  
3/12  3/16/18  N/A  Spring Break 

Test 2 (3/21/18), 3.1  Review, catch up, Test 2 (covers Chapter 2), discrete Fourier transform 

3.1.13.1.4, 3.2.1, Good Friday/Reading day (3/30/2018)  Discrete Fourier transform, fast Fourier transform (FFT), applications, discrete signals & filters 
4.1, 4.2, 4.3  Haar wavelets, decomposition and reconstruction algorithms, filter representation  

5.1, 5.2  Multiresolution analysis (MRA), examples, scaling relation & scaling function, wavelet & wavelet spaces 

5.3.3, Theorem 5.2.3, 6.26.3  Decomposition and reconstruction algorithms, connection with FT, and existence criteria for wavelets, Daubechies wavelets 

Test 3 (4/27/18)  Review, catch up, Test 3 (covers Chapter 4, 5.1, 5.2, 5.3.35.3.4, 6.2) 

6.2  presentations 
Tuesday, 5/8/18  N/A  Projects due at noon 
Updated 1/28/2018.