Notice of RetractionDesign of odd number rational coefficients symmetric compactly-supported biorthogonal wavelet filters

Notice of Retraction

After careful and considered review of the content of this paper by a duly constituted expert committee, this paper has been found to be in violation of IEEE´s Publication Principles.

We hereby retract the content of this paper. Reasonable effort should be made to remove all past references to this paper.

The presenting author of this paper has the option to appeal this decision by contacting TPII@ieee.org.

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.