2-D filter stability tests using polynomial array

A stability table in which F(x,z)= Sigma a/sub j/(x)z/sup j/, for j=0 to n, where a/sub j/(x) are real polynomials of order n/sub 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(z/sub 1/,z/sub 2/), followed by constructing the polynomial array and then applying the appropriate stability test. This procedure is proved to be equivalent to testing F(z/sub 1/,z/sub 2/) directly. A number of examples are given to illustrate the proposed methodology.>