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 function and the realization of a stable single-variable transfer function . Then is the desired 2-variable stable transfer function which is guaranteed to have at least one realization whenever and are realizable. Applications of the theory developed in this paper are presented in the design of lumped-distributed filters and 2-dimensional digital filters.