Multidimensional Signal Processing

Abstract

Abstract : Properties of various multidimensional polynomials arising in studies of passive (lossless) discrete multidimensional systems are investigated. Reactance Schur polynomials and immittance Schur polynomials occurring respectively as the denominators (and numerators) of discrete reactance functions and discrete positive functions are introduced and their properties studied. Role of these polynomials in scattering or immittance descriptions of passive discrete time domain multiports are brought out. The interrelation between classes of multidimensional polynomials arising in discrete systems and the corresponding classes of polynomials in the context of continuous systems is also studied via the mechanics of bilinear transformation. The problem of structurally passive synthesis of multidimensional digital filters of the quarter-plane casual type as an interconnection of more elementary building blocks directly in the discrete domain has been addressed via the factorization of the chain matrix, the hybrid matrix and the transfer function matrix associated with a prescribed multidimensional lossless two-port. By exploiting recent results on the discrete domain representation of such matrices a generalized lossless two-port matrix has been introduced to present all three factorizations in a unified setting. Necessary and sufficient conditions for factorability as well as algorithm for computing these factors when they exist are obtained.