ND POLYNOMIAL-MATRICES WITH APPLICATIONS TO MULTIDIMENSIONAL SIGNAL ANALYSIS

In this paper, different primeness definitions and factorization prope rties, arising in the context of no Laurent polynomial matrices, are i nvestigated and applied to a detailed analysis of no finite support si gnal families produced by linear multidimensional systems. As these fa milies are closed w.r.t, linear combinations and shifts along the coor dinate axes, they are naturally viewed as Laurent polynomial modules o r, in a system theoretic framework, as no finite behaviors. Correspond ingly, inclusion relations and maximality conditions for finite behavi ors of a given rank are expressed in terms of the polynomial matrices involved in the algebraic module descriptions. Internal properties of a behavior, like local detectability and various notions of extendabil ity, are finally introduced, and characterized in terms of primeness p roperties of the corresponding generator and parity check matrices.