Notice of Retraction: Design of odd number rational coefficients symmetric compactly-supported biorthogonal wavelet filters

Abstract

Most wavelet filters that constructed based on Daubechies compactly-supported wavelet construction theory have nonlinear phase and irrational number coefficients. Nonlinear phase may cause distortion in image processing, and irrational filter coefficients will cause much inconvenience for wavelet applications on computer, especially for embedded processor applications. With thought of the theory of perfect-reconstruction filter banks, this paper does a study for linear phase biorthogonal perfect-reconstruction wavelet filter banks, and through of detail derivation, makes a conclusion for the procedure of odd number rational coefficients symmetric compactly-supported biorthogonal wavelet filter construction, which can be achieved by adding some vanishing moments conditions. With the example of length 7-5 biorthogonal wavelet filters design, this paper makes a detail discussion on the value selection for free variable appears in design equations, and then deduces the length 7-5 rational biorthogonal wavelet filters models.