Some results on vanishing moments of wavelet packets, convolution and cross-correlation of wavelets

Abstract

A formula for calculating moments for wavelet packets is derived and a sufficient condition for moments of wavelet packets to be vanishing is obtained. Also, the convolution and cross-correlation theorems for Hilbert transform of wavelets are proved. Finally, using MRA of $L^2\left(R\right)$, some results on the vanishing moments of the scaling functions, wavelets and their convolution in two dimension are given.