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Created page Wavelet.
This is a huge topic, of course...I think one could explain some elementary facts and provide a list to further material, instead of writing a new encyclopedia :-)
@John: If you plan to hire some applied mathematicians over at UCR and create some applied math courses, wavelets are a good candidate for some advanced stuff: This is both very applied (image/signal processing, data compression, statistical estimation, numerical solutions and approximation theory etc.) and very interesting from a pure mathematical point of view (turbulence, fractals, harmonic analysis...).