An efficient numerical scheme to compute 2-D stability thresholds

Stability thresholds (margins) of two-dimensional (2-D) digital filters were recently defined in terms of the singularities of the transfer function. Stability thresholds hold a close relationship to the settling time of the 2-D impulse response and can therefore serve as a measure of stability of 2-D digital filters. In this paper, a simple, unified procedure for the computation of stability thresholds (margins) for 2-D digital filters based on the and resultants of 2-D polynomials is presented. To illustrate the process, simple examples are also provided.