On two-dimensional filter stability test

In this paper, a new procedure of 2-D filter stability test is proposed based on linking and further development of some newly published contributions of the authors. The modified polynomial array given in this paper eliminates redundant information introduced in the ordinary table technique and leads to a great reduction in the order of polynomial entries of the array from n₂2n^{(1/-1) to n} sub 1/n₂, where n₁ and n₂ are the orders of F(z1, z₂), the characteristic polynomial of the filter under test, in z₁ and z₂ respectively. The properties of the array are studied and a systematic construction procedure given. The new test procedure applies twice to the array. The first application involves only numerical entries, but provides a simple way for a primary checking of some necessary conditions before any further complex computations are required. The second application involves constructing of the polynomial array and the positivity testing of only the last entry of the array for all |z₁|=1. The simplicity of the method may allow it to be applied for filter designs