Prerequisite:   MATH 221-222, 223-224, 293-294, or permission of instructor.

General description: The goal of the course is to introduce the student to some basic concepts of Fourier analysis and wavelet theory, as well as to some of their applications in engineering (specifically to signal processing). Topics include: Fourier series, Discrete Fourier analysis, Fourier transform, Shannon sampling theorem, the Haar system, Multiresolution Analysis and wavelets bases. Emphasis will be placed upon understanding and performing mathematical proofs.

Lectures: MWF 11:15 - 12:05, MT 230

Instructor:    Kasso Okoudjou, 411 Malott Hall, kasso@math.cornell.edu, Phone: (607) 255-7244.
Office Hours: Monday 10:00 a.m. - 11:00 a.m., Friday 2:00 p.m. - 3:00 p.m., or by appointment.

Teaching Assistant:    Jason Anema, 120 Malott Hall, janema@math.cornell.edu, Phone: (607) 255 7548.
Office Hours: Tuesday 1:00 p.m. - 2:00 p.m., Wednesday 1:00 p.m. - 2:00 p.m.

Textbook:   A. Boggess & F. J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice Hall, (2001), ISBN 0-13-022809-5.
Additional textbook:   David F. Walnut, An Introduction to Wavelet Analysis, Birkhauser Boston (2002), (ISBN 0-8176-3962-4) is on reserve in the Math Library.

Course web page: http://www.math.cornell.edu/~kasso/math424sp06.html

Homework and Examinations:

• Homework assignments are due in class on Mondays, covering the previous week's material. They will be graded and returned to you. No late homework will be accepted. It is OK to work on the problem sets in cooperation with others, but you must write up the solutions by yourself.
• In addition to the weekly homework assignments, there will be two (in class) mid-term exams and a take home final exam . The tentative schedule for the exams is:
  Prelim 1: Wednesday, March 9.
  Prelim 2: Wednesday, April 20.
  Final: TBA

Grading: Prelims count 25% each, the final 30%, and the homework 20%.

Attendance and absences : You are responsible for the material covered in class, whether you attend or not. You are also responsible for the announcements made during class; they may include changes in the syllabus.

If you need accommodations because of a disability, please inform me immediately.

Tentative Course Outline & Homework assignments

Week	Reading	Homework
1     1/23 - 1/27	Ch.0	Ch.0: no. 3, 4, 6, 7, 10 Due 1/30
2     1/30 - 2/3	1.1, 1.2	Ch0: 14, 15, 16; Ch.1: no. 1, 3, 4, 7, 11, 16, 22, 32 Due 2/6
3     2/6 - 2/10	1.3	Ch.1: no. 15, 17, 18, 19 (a), 23, 28, 29, 33, 34 Due 2/13
4     2/13 - 2/17	2.1, 2.2	Ch.2:no, 1, 2, 3, 4, 5, 6 Due 2/20
5     2/20 - 2/24	2.3, 2.4, 2.5	ch.2, no: 10, 12, 14 Due 2/27
6     2/27 - 3/3	Ch.3	Ch. 3, no. 7, 8, 14, 15 pdf ; ps Due 3/6
7     3/6 - 3/10	4.1, 4.2	Ch. 4, no. 1, 2, 4, 8 Due 3/17
Friday, March 10	Prelim 1	pdf ; ps Due 3/31
8     3/13 - 3/17	4.3	Ch.4, no.: 6, 7, 9, 10, 11 Due 3/27
9     3/20 - 3/24	Spring Break
10     3/27 - 3/31	5.1,5.2	Ch. 5, no.: 3, 4, 6, 8 Due 4/3
11     4/3 - 4/7	5.2, 5.3	Ch. 5, no.: 5, 7, 9, 10 Due 4/10
12     4/10 - 4/14	6.1, 6.2	Ch. 6, no.: 1, 2, Generate the graph of the sacling function and the wavelet corresponding to the N=2 Daubechies wavelet Due 4/17
13     4/17 - 4/21	6.3, 6.4	Ch. 5: 10, 17, 18 Due 4/24
Friday, April 21	Prelim 2
14     4/24 - 4/28	Finite Frames	pdf ; ps Due 5/3
15     5/1 - 5/5	Gabor frames

Data for Problem 2 of the final exam: Real(Real part of the DFT of the image); Imaginary (Imaginary part of the DFT of the image).

Image for Problem 5 of the final exam noisemont.tif