Computer†aided design of stable recursive digital filters from magnitude specifications

This paper presents a method of designing one‐ and two‐dimensional recursive digital filters making use of the properties of bilinear transformation of strictly Hurwitz polynomials. The result is a stable digital filter in both one‐ and two‐dimensional cases, which requires no further testing for stability. The well known unconstrained minimization technique of Fletcher—Powell is used, making use of a transformation of optimization parameters to satisfy the mild constraints of stability. This method is considered to be more efficient on an overall basis than the existing lp design technique of Maria and Fahmy. Nor does it rely on Deczky's theorem to ensure a stable filter which may sometimes lead to unstable solutions in the two‐dimensional case. An example is provided illustrating the method. Copyright © 1979 John Wiley & Sons, Ltd.