Joseph Fourier

Ingrid Daubechies

Fourier and signal analysis: academic year 2005-2006

This is a reading course in the programs master of mathematics and master of mathematical physics of the University of Amsterdam.


The first introductory meeting was on Tuesday February 14, 2006, 16.00-17.00 hour, room P015A, Euclides building.
Next sessions will also be on Tuesday, 16.00-17.00 hour, room to be announced, tentatively P015A.
The session of 18 April will start at 15.30 hour, with presentations by two students on Heisenberg's inequality and on the Discrete and Fast Fourier Transform.

Lecturer:   T.H. Koornwinder


Mathematica Notebooks

The final mark will be based for 50% on submitted exercises (possibly combined with an oral examination about a part of the material on wavelets) and for 50% on the written and oral presentation of a final project.

Schedule for the sessions

(S-S = Stein & Shakarchi, D = Daubechies)

Date Material  Exercises to be submitted
21 Feb. S-S, Ch.2 two from Ex. 2.6, 2.7, 2.8, 2.9, 2.13, 2.14, 2.16, 2.17
or one from Problems 2.1, 2.2
28 Feb. S-S, Ch.3 Ex. 3.16 or two from Ex. 3.8, 3.9, 3.14, 3.18
7 Mar. S-S, Ch.3, §2.2 two from Ex. 4.5, 4.7, 4.8, 4.9
14 Mar. S-S, Ch.3, Ex. 20; Ch.5, §1 one from Ex. 5.1, 5.2 and one from Ex. 5.6, 5.8
21 Mar. S-S, Ch.5, §1 Ex. 1 from More on Fourier integrals
or Ch. 5, Problem 7, (a)-(c) (use my hints in More on Fourier integrals)
4 Apr. S-S, Ch.5, §1,3
18 Apr. Koornwinder's syllabus
Fourier analysis, §10
two students will give presentations
25 Apr. D, Ch.2 and Chapter on Continuous
wavelet transform in Koornwinder's book

to Tom Koornwinder's home page