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

A method is presented for the design of a class of two-dimensional (2-D) stable digital filters satisfying prescribed magnitude of constant group delay specifications. The design method generates a 2-D digital transfer function which is a product of two transfer functions, H1(z1,z2) and H2(z1,z2), corresponding to a recursive filter and a nonrecursive filter, respectively. Component H1(z1,z2) ensures a wave-digital realization, that is, the design method guarantees the generation of a corresponding analog function H1A(s1,s2) which is realizable as the transfer function of a doubly-terminated two-variable lossless network. Thus the design technique ensures that not only a given frequency response is 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 s1-and s2-variable lossless two-ports with all of their transmission zeros at infinity.