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 l_2 and l_1 stabilities of a function G(z_1, z_2)= P(z_1, z_2)/[Q(z_1, z_2)]^n , where P/Q has simple nonessential singularities of the second kind on T^2 , 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.