Fourier Analysis and Wavelets: Math 472
We'll be covering Fourier Series, discrete and infinite, and Fourier intergrals,
in 1-D, and Wavelets (Daubechies and Haar)
and Multiresolution analysis, again in 1-D, and then
move to the 2-D case toward the end of the semester.
concerned with issues like: convergence of Fourier series; the relation
between discrete Fourier transforms
and the infinite Fourier transform; why do Daubechies wavelets exist; and
what is the wavelet transform in JPEG2000.
We'll not spend much time on: why the Fast Fourier Transform is fast; how to
implement filterbanks that perform a
wavelet transform; numerical issues in filtering.
The book is
"A First Course in Wavelets with Fourier Analysis,"
by Albert Boggess and Francis J. Narcowich, ISBN 0-13-022809-5,