2-D digital filter stability in the presence of second kind nonessential singularities

We present two new conditions for the stability of 2-D digital filters in the presence of nonessential singularities of the second kind. The first is a necessary condition expressed in terms of tangents to the algebraic curve at a zero of the denominator polynomial on the distinguished boundary of the unit polydisk. This necessary condition is shown to be preserved under parameter quantization in some cases. The second condition we present is sufficient for stability, and is considerably weaker than that imposed by Goodman.