2-D filter stability tests using polynomial array

Abstract

A stability table in which F(x, z) = Σaj(x)zj, for y = 0 to n, where aj(x) are real polynomials of order n1, 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.