Stabilization of 2D nonsymmetric half-plane digital filters using the concept of reciprocity

Abstract

In this paper, the concept of reciprocity for two-dimensional (2D) quarter plane (QP) filters are extended to stabilize 2D nonsymmetric half-plane (NSHP) filters. In general the stabilization of NSHP filters is done by transforming NSHP arrays into QP arrays using mapping theorems. The concept of reciprocity is applied directly without any mapping to stabilize a class of 2D NSHP filters which are otherwise unstable when all singularities lie within the unit bicircle. It is shown that the magnitude spectrum of the stabilized 2D NSHP filter is identical to the magnitude spectrum of the original unstable filter. The proposed stabilization method is simple as compared to two other popular stabilization techniques in the literature, the double planar least squares inverse (DPLSI) and 2D discrete Hilbert transform (2D DHT).