Two-dimensional biorthonormal wavelet on ZN1 × ZN2

In this paper, Fourier analysis are first presented in the two-dimensional context. Then existing work on the representation of wavelets on Z
N
is extented to two dimensions. A necessary and sufficient condition on the existence of biorthonormal wavelets on Z
N1
× Z
N2
is derived. A method for constructing biorthonormal wavelest on Z
N1
× Z
N2
is presented and their properties is investigated by mean of time-frequency analysis method, matrix theory and operator theory.