A simple stability criterion for nonlinear multi-dimensional (M-D) direct form digital filters

A simple algebraic stability condition for m-D nonlinear digital filters is derived. The proof is based on a comparison between a linear positive coefficient filter and the associated nonlinear filter. The test condition involves the denominator coefficients of the linear comparison filter in a simple form. The application of these results to first-order m-D filters proves the preservation of stability under a large class of finite wordlength operations. Furthermore a class of arbitrary-order m-D stability preserving filters under finite wordlength arithmetic is constructed