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.