An algorithm for testing stability of two-dimensional digital recursive filters

The Principle of the Argument is applied to test the stability of a 2-D recursive filter with denominator B(Z 1 ,Z 2 ). This approach to stability testing leads to an efficient numerical implementation requiring only the computation of a 2-D DFT, followed by phase unwrapping and a search for zeros of B(e^{j\omega_{1}},e^{j\omega_{2}}) . In the absence of zeros of B(e^{j\omega_{1}},e^{j\omega_{2}}) , stability is assured if B(Z 1 ,1) and B(1,z 2 ) are both minimum phase.