Two-dimensional periodic discrete wavelets bases

Abstract

In this paper, Fourier analysis are first presented in the two-dimensional context. Then existing work on the representation of wavelets on ZN is extended to two dimensions. A necessary and sufficient condition on the existence of wavelets on ZN1 × ZN2 is derived. A method for constructing wavelets on ZN1 × ZN2 is presented and their properties is investigated by mean of time-frequency analysis method, matrix theory and operator theory.