Applications of the fast wavelet transform
Christopher E. Heil · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1990
The fast wavelet transform is an order-N algorithm, due to S. Mallat, which performs a time and frequency localization of a discrete signal. It is based on the existence of orthonormal bases ( for the space of finite-energy signals on the real line) which are constructed from translates and dilates of a single fixed function, the "mother wavelet" (the Haar system is a classical example of such a basis; recent continuous examples with compact support are due to I. Daubechies). We discuss the derivation of the Mallat wavelet transform, give some examples showing its potential for use in edge detection or texture discrimination, and finally discuss how to generate Daubechies' orthonormal bases.