Approximation of two-variable filter specifications in analog domain

This paper describes a technique for approximating 2-variable filter specifications in the continuous or analog domain. It is shown that the design of 2-variable filter functions using this approach reduces to the problem of identifying a suitable 2-variable reactance functiong(s_1,s_2)and the realization of a stable single-variable transfer functionT(s). ThenT(g(s_1,s_2))is the desired 2-variable stable transfer function which is guaranteed to have at least one realization wheneverT(s)andg(s_1,s_2)are realizable. Applications of the theory developed in this paper are presented in the design of lumped-distributed filters and 2-dimensional digital filters.