Abstract
Abstract Any algorithm for testing the stability of 2-D digital recursive filters has to process a 2-D polynomial of degree n and m with respect to each variable. The number of computations needed by the algorithm can be expressed as a polynomial of the variables n and m . The total degree of this polynomial defines the complexity order of the algorithm. In this paper we establish that the matrix associated with Bezout's resultant appearing in the stability test of causal or semicausal recursive filters has 2 as its displacement rank. This permits us to apply the generalized Levinson-Szego algorithm to derive a new algorithm for testing the 2-D digital filters' stability. This algorithm is proposed for quarter-plane or nonsymmetric half-plane recursive filters with real coefficients and without nonessential singularities of the second kind. Its complexity order is equal to 4. Note that the complexity order of the fastest existing algorithms is equal to 5.
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