1 Math 472/572 - Fourier analysis and wavelets


Fall 2007

This class is cross-listed as:

This course is an introduction to Fourier Analysis and Wavelets. It has been specifically designed for engineers, scientists, and mathematicians interested in the basic ideas underlying Fourier analysis, wavelets and their applications.
This course integrates the classical Fourier Theory with its latest offspring, the Theory of Wavelets. Wavelets and Fourier analysis are invaluable tools for researchers in many areas of mathematics and the applied sciences, to name a few: signal processing, statistics, physics, differential equations, numerical analysis, geophysics, medical imaging, fractals, harmonic analysis, etc. It is their multidisciplinary nature that makes these theories so appealing.

Topics will include:

Numerical experiments are necessary to fully understand the scope of the theory. The use of some Wavelet Toolbox will be encouraged. There exists a WAVELAB package which is Matlab/Octave based software designed by a team at Stanford and available for free on the Internet. MATLAB 7.2 is available in the Mathematics and Statistics Department Computer Laboratory (I think).

Grades: Grades will be based on homeworks, projects and/or take-home exams.

Prerequisites: Linear algebra and advanced calculus, or permission from the instructor.

Textbook: We will be using a preliminary version of a book that I am writing with my colleague Lesley Ward from University of South Australia. I will be posting chapters on the course webpage as the semester evolves. The book is called Harmonic Analysis: From Fourier to Haar. I appreciate all the feedback I can get from you, because now is our opportunity to make meaningful changes before the book goes into print.

Recommended Texts:

There are many excellent books devoted to the classical theory of Fourier analysis (starting with A. Zygmund's Trigonometric Series , and following with a long list). In the last ten years there have been published a number of books on wavelets, as well as countless articles. Here is a limited guide:

More Mathematical More applied/friendlier For a wider audience or emphasis on applications There is a wealth of information available at wavelet digest

Return to: Department of Mathematics and Statistics, University of New Mexico

Last updated: August 15, 2007