Finite support 2-D FIR QMF PR filter bank design by spectral factorization using Gröbner basis

In this paper, the application of spectral factorization by using Grobner basis approach to the problem of 2-D finite support QMF filter bank design is proposed along with illustrative example. Earlier, it has been shown that the Grobner basis can be applied to solve the problem of 2-D factorization and its effectiveness in dealing with polynomial equation system are demonstrated. Despite the fact that there exist many good techniques for designing one dimensional QMF synthesis and analysis filter banks, the two-dimensional counterpart has a major bottleneck due to the generalization of 2-D spectral factorization. The proposed algorithm is the direct generalization of the 1-D QMF filter bank design by spectral factorization. Furthermore, the filter coefficients can be computed in symbolic forms and thus provide a good opportunity for further optimization if additional criteria are given.