The design of compactly supported orthonormal wavelets with integer scaling factors

Abstract

It has been shown that discrete-time orthonormal wavelet decompositions are related to lossless perfect reconstruction (PR) multirate filter banks except that such filters are not generally designed with wavelet regularity considerations in mind. The authors present a method, based on the design of M-band PR filters, to generate orthonormal wavelets with arbitrary integer scaling factor M, such that the wavelets are regular and the corresponding PR filters have good stop- and pass-band responses. Applications for such filters include the analysis of signals with arbitrary scaling, such as fractals.<>