Design of multidimensional filter banks using Grobner bases: a survey

This paper surveys on the design of multidimensional filter banks using Grobner bases. As multidimensional filter banks can be represented by multivariate rational matrices, Grobner bases are very effective tool in dealing with multidimensional filter banks. While there are several methods for designing multidimensional filter banks using Grobner bases, we point out the feasibility of designing two classes of causal, stable, perfect reconstruction multidimensional IIR filter banks by exploiting results in multidimensional feedback control system design.