Design of Orthogonal Filterbanks with Rational Coefficients Using Grobner Bases

Filterbanks are widely used in many applications. In the literature, most filterbanks with irrational value coefficients were designed, while in practice, filters and filterbanks are implemented using rational coefficients. This paper introduces a powerful mathematical tool called Grobner basis (GB) into the design of orthogonal filterbanks. Specifically, we use GB to find good rational lattice parameters for Daubechies length 6 (Db6) filterbank. We show that there does not exist any Db6 filterbank with rational coefficients and also meeting the first two vanishing moments (VM's). Moreover, we obtain several good Db6 filterbanks which meet the first VM exactly and the second VM approximately.