Stability of a class of 2-D recursive filters without distortion of the amplitude spectrum

Abstract

In this paper, we introduce the concept of reciprocity for two-dimensional (2-D) polynomials, and it is shown that a 2-D polynomial and its reciprocal have the same amplitude spectra. This concept is applied to stabilize a class of 2-D recursive filters being unstable due to all singularities occuring within the unit hypercircle. This method is simple and provides a stabilized filter without any distortion of the amplitude spectrum. Before bringing up any other technique of stabilization this method should be tried.