Stability testing of 2-D recursive digital filters based on a circuit-theoretic approach

A procedure for checking the stability of 2-D digital filters is proposed. The key part of the test involves construction of related all-pass sections of reduced order, the stability of which is shown to be equivalent to the stability of the original function. This is a direct extension of a similar approach, developed recently (1987) by P.P. Vaidyanathan and S.K. Mitra, in detail for the 1-D case. The results are shown to be equivalent to some known stability testing methods in 2-D, but have the advantage of an additional insight gained from the circuit interpretation. Explicit formulas for checking the stability in terms of the filter coefficients are derived for some special cases, and numerical examples are included to clarify the application of the proposed approach.<>