The wavelet transform is actually as a set of techniques for generating orthonormal bases suited to particular problem domains. These techniques originally developed independently in several fields, including pure mathematics [Calderón], physics [Aslaksen and Klauder] [Paul], seismic analysis [Morlet], and of course in engineering [Esteban and Galland], [Smith and Barnwell]. A recent synthesis has brought these different approaches together. The result is a rich toolkit with applications in spectral analysis, signal processing, data compression, and transformational algebras, to name a few.