Realization of resistively terminated two-variable lossless ladder networks

Abstract

A major problem to be solved in the design of two-dimensional wave digital filters is the realization of a resistively terminated two-variable analog reference network satisfying the prescribed specifications. This paper presents a simple procedure for the realization of a two-variable doubly (resistively) terminated low-pass ladder network with all transmission zeros at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{1} = \infty</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s_{2} = \infty</tex> (in the complex <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{S_{1}, S_{2}\}</tex> biplane). The transfer function of the realized network will not have nonessential singularities of first or second kind in the closed right half of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\{S_{1}, S_{2}\}</tex> planes including infinite distant points, so the analog network realized can be converted into a 2-D wave digital filter with guaranteed stability. The realization is obtained using the two-variable approach.