Stability test for two-dimensional recursive filters

For deciding the stability of a two-dimensional filter, it is of interest to determine whether or not a prescribed polynomial in the variables z1and z2is nonzero in the region|z₁| ≤ 1 ∩ |z₂| ≤ 1. A new procedure for testing for this property is given, which does not involve the use of bilinear tranformations. Key parts of the test involve the construction of a Schur-Cohn matrix and the checking for positivity on the unit circle of a set of self-inversive polynomials.