The objective here is to underscore recent usage of the algorithmic theory
of Grobner bases in multidimensional systems since that possibility was hig
hlighted about fifteen years back. The main contribution here focuses on th
e constructive aspects of the solution, known to exist, of the two-band mul
tidimensional IIR perfect reconstruction problem using Grobner bases. Other
recent research results on the subject with future prospects are also brie
fly cited.