Publication

Groebner bases and multidimensional FIR multirate systems

Martin Vetterli
1997
Journal Articles

Abstract

The polyphase representation with respect to sampling lattices in multidimensional (M-D) multirate signal processing allows us to identify perfect reconstruction (PR) filter banks with unimodular Laurent polynomial matrices, and various problems in the design and analysis of invertible MD multirate systems can be algebraically formulated with the aid of this representation. While the resulting algebraic problems can be solved in one dimension (1-D) by the Euclidean Division Algorithm, we show that Gröbner bases offers an effective solution to them in the M-D case.

Official source

https://infoscience.epfl.ch/entities/publication/93cd77f0-0032-473d-a726-5b562f4e5280

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Martin Vetterli
1997
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/93cd77f0-0032-473d-a726-5b562f4e5280

About this result

Related concepts (31)

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In signal processing, a filter bank (or filterbank) is an array of bandpass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal.

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Algebraic geometry is a branch of mathematics which classically studies zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical problems about these sets of zeros. The fundamental objects of study in algebraic geometry are algebraic varieties, which are geometric manifestations of solutions of systems of polynomial equations.

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Related publications (2)

Groebner bases and multidimensional FIR multirate systems

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