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

In this paper, the open problem regarding the BIBO stability of two-dimensional linear shift invariant filters, in the presence of nonessential singularities of the second kind, is considered. Necessary and sufficient conditions for boundedness, and and stabilities of a function , where has simple nonessential singularities of the second kind on , are obtained. These conditions are expressed in a very simple way in terms of the multiplicity of the zeros of certain resultants of two-variable polynomials. Many illustrative examples are also given.