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. Another software available for free is KHOROS which has been designed at EECE/UNM and Los Alamos. MATLAB, in particular the Wavelets Toolbox, is available on the University computer system. MATLAB 6 is available in the Mathematics and Statistics Department Computer Laboratory.
Texts:
Grades: Grades will be based on homeworks, projects and/or take-home exams.
Prerequisites: Linear algebra and advanced calculus, or permission from the instructor.
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. There is a wealth of information available at wavelet digest
Return to: Department of Mathematics and Statistics, University of New Mexico
Last updated: August 16, 2001