Let us consider a recursive filter of transfer function H(z) = B(z)/A(z) that is causal or semi-causal and without non-essential singularity of the second kind in the unit bi-circle T2. We write:
In this section, we ask these question: “how do we choose a criterion to test the stability of H(z) Is there a criterion that is better adapted than the others for computer implementation?”
To answer these questions, we will introduce the complexity degree of a 2-D stability criterion and show that certain criteria have a minimum degree of complexity.
We saw at the end of Chapter 10 that the resultant R(z1) obtained by eliminating z2 between the two polynomial equations in z2:
is a complex polynomial in the variables z1 and whose coefficients ...