Transfer function realization of a class of doubly-terminated two-variable lossless networks and their application in linear-phase 2-dimensional digital filter design

Abstract

A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude and constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions H 1 ( z 1 , z 2 ) and H 2 ( z 1 , z 2 ), corresponding to a recursive filter and a nonrecursive filter, respectively, Component H 1 ( z 1 , z 2 ) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H 1A ( s 1 , s 2 ) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only is a given frequency response achieved, but also the generated transfer function is realizable as a cascade of a wave-digital filter and a nonrecursive digital filter. The class of filters considered here is one in which the doubly-terminated analog network used to realize the wave digital filter is a cascade of s 1 - and s 2 -variable lossess two-ports with all their transmission zeros at infinity.