Piecewise periodized wavelet transform and its realization, properties and applications

Abstract

In this paper, the realization of piecewise periodized wavelet transform (PPWT) is introduced and some interesting properties are discussed. The signals in both the time and frequency domains are of finite length. The inverse of the transform exists if the inverse of all the N wavelet kernels exist. Under certain conditions, a time shift of the input leads to a shift in the output of another non-uniform filter bank sub-system. The frequency response of each non-uniform filter bank sub-system consists of a set of frequency components with fundamental frequency different from the input frequency. Some applications, such as adaptive regional image processing techniques, analysis of aperiodic switching systems, and design of frequency to voltage converters, are readily facilitated by the transform.