2-D filter stability tests using polynomial array

A stability table in which F(x,z)=Σa_j(x )z^j, for j=0 to n, where a_j(x) are real polynomials of order n ₁, called a polynomial array, is presented, and a systematic procedure for constructing its entries is given. The polynomial array is then used to test the stability of 2-D filters. This is accomplished by first forming a polynomial with real coefficients from the 2-D filter characteristic polynomial F(z₁,z₂), followed by constructing the polynomial array and then applying the appropriate stability test. This procedure is proved to be equivalent to testing F(z₁,z₂) directly. A number of examples are given to illustrate the proposed methodology