nD polynomial matrices with applications to multidimensional signal analysis

In this paper, different primeness definitions and factorizationproperties, arising in the context of nD Laurentpolynomial matrices, are investigated and applied to a detailedanalysis of nD finite support signal families producedby linear multidimensional systems. As these families are closedw.r.t. linear combinations and shifts along the coordinate axes,they are naturally viewed as Laurent polynomial modules or, ina system theoretic framework, as nD finite behaviors.Correspondingly, inclusion relations and maximality conditionsfor finite behaviors of a given rank are expressed in terms ofthe polynomial matrices involved in the algebraic module descriptions. Internal properties of a behavior, like local detectability andvarious notions of extendability, are finally introduced, andcharacterized in terms of primeness properties of the correspondinggenerator and parity check matrices.