A new stability test theorem of 2-dimensional recursive digital filters and it´s application

A theorem of stability test of two-dimensional recursive digital filters is presented. It is very convenient to test the stability of two-dimensional digital filters by applying the theorem. The closed form stable region of the filters´ coefficients also can be determined. An efficient method derived from the theorem is presented to test the stability of the digital filters with nonlinearities such as quantization, overflow, saturation, etc. Examples to illustrate the application of the theorem are given