On the optimality of the classical stability criteria for 1-D and 2-D digital recursive filters

摘要

A bound for the complexity of any algebraic criterion, giving necessary and sufficient conditions for the stability of digital recursive filters, is proposed in the 1-D and 2-D cases. It is shown that the set of the 1-D Schur polynomials with a degree not greater than n, in the (n+1)-dimensional space of the polynomial coefficients, is convex and its boundary is a hypersurface which has an irreducible equation.