Design of basic elements of multidimensional multirate systems. Multidimensional filters with fractional shift

Abstract

The problem of designing filter banks for multidimensional multirate systems by using a lifting technique is considered. To solve it, we develop a design method for multidimensional digital filters with fractional shift. A symmetric structure is defined for τ = (1/2, 1/2) and a new structure is designed based on application of multidimensional Taylor series. Frequency and impulse responses are given for filters with fractional space shift and their L 2-norm is found. Relevant wavelet functions are calculated and results of image compression by the designed filter banks are presented.