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
g(s_1,s_2)
and the realization of a stable single-variable transfer function
T(s)
. Then
T(g(s_1,s_2))
is the desired 2-variable stable transfer function which is guaranteed to have at least one realization whenever
T(s)
and
g(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.