Wavelet Filter Banks and Applications

Abstract

Traditionally wavelet basis is an orthonormal basis of L²(R), which is formed by translations and dilations of a single wavelet function which is usually known as the mother wavelet. After Mallat and Meyer developed multiresolution analysis, the relationship of wavelet bases to filter bank theory was established. Multiresolution analysis introduced a new function called scaling function. It also enabled us to first design the scaling function and then complete the filter bank to obtain the wavelet function. Probably the most important notions wavelets added to the filter bank theory are vanishing moments and regularity.