ABSTRACT
This chapter explores periodic wavelet transforms. In many practical applications, the functions to be transformed are defined on a compact set. An immediate solution to this problem of data on a compact set is to pad the data with zeros, and apply the wavelet theory developed on the real line. However, this scheme introduces discontinuities at the end points of the interval. The chapter examines computational complexity of the fast periodic wavelet transform. It discusses further, a matrix formulation of the fast periodic wavelet transformation. The chapter provides algorithms for fast periodic wavelet transform and its inverse. Periodic functions can be expanded in terms of periodic scale functions and periodic wavelets. The chapter describes computational complexity of the fast periodic wavelet transform. It is assumed that a multiplication operation is more expensive than an addition operation. It is instructive to obtain a matrix formulation of the fast periodic wavelet transformation.
