Approximate moments and regularity of efficiently implemented orthogonal wavelet transforms

An efficient implementation of orthogonal wavelet transforms is obtained by approximating the rotation angles of the orthonormal rotations used in a lattice implementation of the filters. This approximation preserves the orthonormality of the transform exactly but leads to non-vanishing moments (except of the zeroth moment). The regularity of these wavelets is analysed by exploiting their finite scale regularity, i.e. “smoothness” only up to a certain finite scale. This finite scale regularity is also related to classical filter banks