A Tutorial on GrÖbner Bases With Applications in Signals and Systems

Abstract

This paper is a tutorial on Grobner bases and a survey on the applications of Grobner bases in the broad field of signals and systems. A reasonably detailed review is given of several fundamental theoretical issues that occur in the use of Grobner bases in multidimensional signals and systems applications. These topics include the primeness of multivariate polynomial matrices, multivariate unimodular polynomial matrix completion, and prime factorization of multivariate polynomial matrices. A brief review is also presented on the wide-ranging applications of Grobner bases in multidimensional as well as one-dimensional circuits, networks, control, coding, signals, and systems and other related areas like robotics and applied mechanics. The impact and scope of Grobner bases in signals and systems are highlighted with respect to what has already been accomplished as a stepping stone to expanding future research.