Course

Basic Properties of the Discrete Fourier Transform, Translation-Invariant Linear Transformations. The Fast Fourier Transform.

Construction of Wavelets on ??_??, The First Stage Construction of Wavelets on ??_??, The Iteration Step.

Examples and Applications, ??2(??),

Complete Orthonormal Sets in Hilbert Spaces, ??₂([−??, ??)) and Fourier Series, The Fourier Transform and Convolution on ??₂(??), First-Stage Wavelets on ??

The Iteration Step for Wavelets on Z, Implementation and Examples.

??₂(??) and Approximate Identities, The Fourier Transform on ??, Multiresolution Analysis and Wavelets, Construction of Multiresolution Analyses, Wavelets with Compact Support and Their Computation.

References:

1. Michael Frazier, An Introduction to Wavelets Through Linear Algebra, Springer,1999.
2. Daubechis, Ten Lectures on Wavelets, SIAM, Mallat, S. A Wavelet Tour of Signal Processing, Elsevier, 2008