On Constructing Regular Filter Banks From Domain Bounded Polynomials

The design of regular two channel bi-orthogonal filter banks is shown to be reducible to the design of pairs of real polynomials with domain bounded to the interval [-1,1]. Techniques for designing polynomials satisfying various constraints are outlined. Transformation of polynomials to multidimensional bi-orthogonal filter banks is presented. Keywords--- Polynomials, digital filter, filter banks, perfect reconstruction, bi-orthogonal. EDICS Nr---Filter Bank Theory 2.4.2 I . Introduction In this correspondence we will be concerned with the design of critically sampled, 2-channel, zero phase bi-orthogonal (BO) filter banks (FB) [3] [17]. The approach we follow is to reduce the design of 1-D zero phase BO FB to the design of appropriate real polynomials on the interval [-1,1]. These polynomials are then transformed to yield 1-D and also multidimensional (m-D) zero phase BO FB. A 1-D biorthogonal filter bank of the above class is characterized by the pair of filters fG 0 ; H 0 g in the ..