Circular convolution, translation invariant linear transformations. Fourier series and wavelets in sequence space. Multiresolution analysis on the line. Meyer's, Shannon's and Daubechies' compactly supported wavelets. Biorthogonal wavelets, wavelet packets, wavelets on the interval.
Numerical experiments are necessary to fully understand the scope of the theory.
The use of some Wavelet Toolbox will be encouraged. An Introduction to Wavelets Through Linear Algebra by Michael Frazier . Fourier series and integrals by H. Dym and H.P. McKean. In the last ten years there have been published a number of books on wavelets, as well as countless articles.