Fourier Analysis and Wavelets:  Math 472

UNM, Fall '003, Professor Terry A. Loring

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.

We'll be 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, Pentice Hall

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