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Multidimensional FIR filter bank design using Grobner bases

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2 Author(s)
Charoenlarpnopparut, C. ; Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA ; Bose, N.K.

A multivariate polynomial matrix factorization algorithm is introduced and discussed. This algorithm and another algorithm for computing a globally minimal generating matrix of the syzygy of solutions associated with a polynomial matrix are both associated with a zero-coprimeness constraint that characterizes perfect-reconstruction filter banks. Generalizations, as well as limitations of recent results which incorporate the perfect reconstruction as well as the linear-phase constraints, are discussed with several examples and counterexamples. Specifically, a Grobner basis-based proof for perfect reconstruction with linear phase is given for the case of two-band multidimensional filter banks, and the algorithm is illustrated by a nontrivial design example. Progress and bottlenecks in the multidimensional multiband case are also reported

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Circuits and Systems II: Analog and Digital Signal Processing, IEEE Transactions on  (Volume:46 ,  Issue: 12 )