Stabilization of Certain Two-Dimensional Recursive Digital Filters

Abstract

A possible extension of a well-known stabilization technique for one-dimensional recursive digital filters to the two-dimensional case was proposed by Shanks via a conjecture, stating that the planar least squares inverse of a two-dimensional filter polynomial is minimum phase and hence stable. In the present work, the conjecture has been verified first for a class of polynomials which are linear in one variable and quadratic in the other and then extended to a class of polynomials of higher degrees in the same variables. Though the conjecture is known to be false, in general, some conditions under which the conjecture is valid are explored. Show more