Stability analysis of multidimensional (m-D) direct realization digital filters under the influence of nonlinearities

A stability test of m-D direct realization digital filters with nonlinearities such as quantization, overflow, saturation, etc., is presented. The method presented reduces a given nonlinear m-D system to a nonlinear 1-D system such that the stability of the latter is sufficient for the stability of the former. To check stability of the nonlinear 1-D system, some new results on 1-D recursive systems with positive coefficients are applied. The case of multiple nonlinearities in multidimensions is also addressed. Examples are given illustrating the application of the method.>