Wavelets and Fourier Series

Wavelets and Fourier Series - Math 424 - Spring 2005

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 406

Instructor: Kasso Okoudjou, 411 Malott Hall, kasso@math.cornell.edu, Phone: 255-7244.
Office Hours: Monday 3:00 p.m. - 4:00 p.m., Wednesday 2:00 p.m. - 3:00 p.m., or by appointment.

Teaching Assistant: Vadims Moldavskis, 120 Malott Hall, vsm7@cornell.edu, Phone: 255 7548.
Office Hours: Thursday 1:30 p.m. 3:30 p.m.; 218 Malott Hall.

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: Math 424 Wavelets and Fourier Series

Homework and Examinations:

Homework assignments are due in class on Fridays, 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: 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 1/24 - 1/28 Ch.0
Ch.0:6, 7, 10, 11, 14, 15, 16
Due 2/2

2 1/31 - 2/4 1.1, 1.2 Ch.1: 1, 3, 4, 7, 16, 22
Due 2/11

3 2/7 - 2/11 1.3 Ch.1: 17, 18, 19 (a), 19(b), 23, 29
Due 2/18

4 2/14 - 2/18 2.1, 2.2 PDF; PS
Due 2/25

5 2/21 - 2/25 2.3, 2.4, 2.5 PS
PDF
PDF Solution HW 4

6 2/28 - 3/4 Ch.3 See last week hw

7 3/7 - 3/11 4.1, 4.2 See next week hw

Wednesday, March 9 Prelim 1

8 3/14 - 3/18 4.3 Ch.4: 1, 4, 6, 7
Due 4/1

9 3/28 - 4/1 5.1,5.2 Ch. 5: 3, 4, 6, 8
PDF Solution

10 4/4 - 4/8 5.2, 5.3 Ch. 5: 5, 7, 9, 10
PDF Solution

11 4/11 - 4/15 6.1, 6.2 Ch. 6: 1, 2, Generate the graph of the sacling
function and the wavelet corresponding
to the N=2 Daubechies wavelet
Due 4/22

12 4/18 - 4/22 6.3, 6.4 Ch. 5: 10, 17, 18
Due 4/29

Friday, April 22 Prelim 2

13 4/25 - 4/29 7.1, 7.2 No HW

14 5/2 - 5/6 No HW

Week	Reading	Homework
1 1/24 - 1/28	Ch.0	Ch.0:6, 7, 10, 11, 14, 15, 16 Due 2/2
2 1/31 - 2/4	1.1, 1.2	Ch.1: 1, 3, 4, 7, 16, 22 Due 2/11
3 2/7 - 2/11	1.3	Ch.1: 17, 18, 19 (a), 19(b), 23, 29 Due 2/18
4 2/14 - 2/18	2.1, 2.2	PDF; PS Due 2/25
5 2/21 - 2/25	2.3, 2.4, 2.5	PS PDF PDF Solution HW 4
6 2/28 - 3/4	Ch.3	See last week hw
7 3/7 - 3/11	4.1, 4.2	See next week hw
Wednesday, March 9	Prelim 1
8 3/14 - 3/18	4.3	Ch.4: 1, 4, 6, 7 Due 4/1
9 3/28 - 4/1	5.1,5.2	Ch. 5: 3, 4, 6, 8 PDF Solution
10 4/4 - 4/8	5.2, 5.3	Ch. 5: 5, 7, 9, 10 PDF Solution
11 4/11 - 4/15	6.1, 6.2	Ch. 6: 1, 2, Generate the graph of the sacling function and the wavelet corresponding to the N=2 Daubechies wavelet Due 4/22
12 4/18 - 4/22	6.3, 6.4	Ch. 5: 10, 17, 18 Due 4/29
Friday, April 22	Prelim 2
13 4/25 - 4/29	7.1, 7.2	No HW
14 5/2 - 5/6		No HW