Grobner bases and applications in the design of multidimensional iir filter banks

Abstract

In this paper, we first give a tutorial on the Grobner bases method. Then it is shown that existing results in multidimensional (nD) feedback control theory using Grobner bases can be applied to the design of two classes of nD causal, stable, perfect reconstruction IIR filter banks. We give an elementary treatment on Grobner bases here, in the hope that it will further bring awareness of and stimulate interest in Grobner bases among researchers in signal and image processing in general, and in the design of nD IIR filter banks in particular.