Math 671: Numerical Analysis - Wavelets - Fall 1996
2842 East Hall,
Time and Location: MW, 8:45-10am, 3439 Mason Hall
Wavelets provide a new way
of representing signals
using translation and scaling.
In some cases,
wavelet expansions have better properties
than classical orthogonal bases.
the November 1995 issue of the
AMS Notices has an article explaining why
switched from a discrete cosine transform
to a wavelet algorithm
for compressing fingerprint data.
This course will present the basic theory
computer implementation of algorithms for
We start with techniques from Fourier analysis
and progress to wavelets.
The topics include:
discrete Fourier transform,
fast Fourier transform,
local Fourier transform,
orthogonal and biorthogonal wavelets,
discrete wavelet transform,
wavelet representation of distributions,
differential and integral equations,
The aim of the course
is to bring students to the point where they
know enough about wavelets
to read the current literature
to consider using wavelets in their own research.
Adapted Wavelet Analysis from Theory to Software
by Victor Wickerhauser,
A. K. Peters Publishing Co.
Ten Lectures on Wavelets,
by Ingrid Daubechies,
Wavelets and Other Orthogonal Systems with Applications,
by Gilbert Walter,
Wavelets and Filter Banks,
by Gilbert Strang and Truong Nguyen,
Students should have a good background in linear algebra.
Some familiarity with
Fourier series, Fourier transform and
will be helpful,
also basic programming skills
(e.g. input/output, arrays, if-then-else, loops, plotting).
I'll use a C pseudocode to present the
but assignments may be done in any language
(e.g. Fortran, C, Matlab, ......).
I plan to review the math and programming prerequisites
depending on the level of the students.
Homework will be assigned,
including programming exercises.