Polynomial inverses of 2D transfer matrices and finite memory realizations via inverse systems

Laurent Polynomial Inverse Matrices and Multidimensional Perfect Reconstruction Systems

We study the invertibility of M -variate polynomial (respectively : Laurent polynomial) matrices of size N by P . Such matrices represent multidimensional systems in various settings including filter banks, multipleinput multiple-output systems, and multirate systems. Given an N × P polynomial matrix H(z) of degree at most k, we want to find a P × N polynomial (resp. : Laurent polynomial) left ...

Computing Moore-Penrose Inverses of Ore Polynomial Matrices

Inverses of Multivariate Polynomial Matrices using Discrete Convolution

A new method for inversion of rectangular matrices in a multivariate polynomial ring with coefficients in a field is explained. This method requires that the polynomial matrix satisfies the one-to-one mapping criteria defined in [1].

Drazin inverse of one-variable polynomial matrices

There is proposed a representation of the Drazin inverse of a given polynomial square matrix, based on the extension of the Leverrier-Faddeev algorithm. Also, an algorithm for symbolic computation of the Drazin inverse of polynomial matrix is established. This algorithm represents an extension of the papers [5], [7] and a continuation of the papers [8], [9], [10]. The implementation is develope...

On the structure of finite memory and separable 2D systems

Several characterizations of finite memory and separability properties for a 2D system are presented, in terms of both the characteristic polynomial and the matrix pair that describes the state evolution. Necessary and sufficient conditions for a finite memory or separable 2D system to have an inverse with the same properties are given; these involve only the structure of the transfer matrix.