Gröbner Bases and Multidimensional FIR Multirate Systems

Authors:
Hyungju Park;Ton Kalker;Martin Vetterli
Affiliations:
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309;Philips Research Laboratories, Prof. Holstlaan 4, 5656 AA, Eindhoven, The Netherlands;Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA 94720
Venue:
Multidimensional Systems and Signal Processing
Year:
1997

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Abstract

The polyphase representation with respect to sampling lattices inmultidimensional (M-D) multirate signal processing allows usto identify perfect reconstruction (PR) filter banks with unimodularLaurent polynomial matrices, and various problems in the designand analysis of invertible MD multirate systems can be algebraicallyformulated with the aid of this representation. While the resultingalgebraic problems can be solved in one dimension (1-D) by theEuclidean Division Algorithm, we show that Gröbner basesoffers an effective solution to them in the M-D case.