nD Polynomial Matrices with Applications to MultidimensionalSignal Analysis

Authors:
Ettore Fornasini;Maria Elena Valcher
Affiliations:
Dip. di Elettronica ed Informatica, Univ. di Padova, via Gradenigo 6a, 35131 Padova, Italy;Dip. di Elettronica ed Informatica, Univ. di Padova, via Gradenigo 6a, 35131 Padova, Italy
Venue:
Multidimensional Systems and Signal Processing
Year:
1997

Citing 1
Cited 13

Multidimensional Systems with Finite Support Behaviors: Signal Structure, Generation, and Detection

SIAM Journal on Control and Optimization

Notes on \sl n-D Polynomial Matrix Factorizations

Multidimensional Systems and Signal Processing
Modules and Behaviours in nD Systems Theory

Multidimensional Systems and Signal Processing - Recent progress in multidimensional control theory and applications
On the Decomposition of Two-Dimensional Behaviors

Multidimensional Systems and Signal Processing - Recent progress in multidimensional control theory and applications
First–Order Representations of Discrete Linear MultidimensionalSystems

Multidimensional Systems and Signal Processing
Some Results on the Relationship Between Two-Dimensional Behaviors Decompositions and the Factor Skew-Primeness Property

Multidimensional Systems and Signal Processing
Two-dimensional behavior decompositions with Finite-Dimensional Intersection: A Complete Characterization

Multidimensional Systems and Signal Processing
Observer-based Fault Detection and Isolation for 2D State-space Models

Multidimensional Systems and Signal Processing
Dead-beat estimation problems for 2D behaviors

Multidimensional Systems and Signal Processing
Optimization of synthesis oversampled complex filter banks

IEEE Transactions on Signal Processing
Notes on factor prime factorizations for n-D polynomial matrices

Multidimensional Systems and Signal Processing
Algebraic decoder of multidimensional convolutional code: constructive algorithms for determining syndrome decoder and decoder matrix based on Gröbner basis

Multidimensional Systems and Signal Processing
Lyapunov stability analysis of higher-order 2-D systems

Multidimensional Systems and Signal Processing
Locally invertible multivariate polynomial matrices

WCC'05 Proceedings of the 2005 international conference on Coding and Cryptography

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.