Biorthogonal Wavelet Filter Banks Design And Application Research

The wavelet filter is a important tool for the wavelet analysis theory in the actual project application. Along with the widespread applications of wavelet transform in pattern recognition, image compression, pronunciation code and information hideaway, the wavelet filter design become more and more important in recent years. Especially in the compression of image and signal, the wavelet transform will substitute for the traditional DCT transform by its superior time frequency analysis characteristic. However, the theory of wavelet is very short since wavelet was put forward, so the wavelet filter design still has many problems need to consummate. Therefore, this article has analyzed the essential method of the wavelet filter design, in this foundation, we have research and improve thoroughly the biorthogonal wavelet filter group which are used most commonly in the process of image and signal.The main important work of this paper:1. Deeply studied wavelet analysis theory and wavelet filter banks design technology.2. In view of the coefficients of CDF9/7 wavelet filter are irrational number, we use the trigonometric function transform to factorize the perfect restruction and the biorthogonal conditions of biorthogonal wavelets filter banks, then optimize the coefficients of the original 9/7 wavelet filter banks, consequently a novel 9/7 wavelet filter banks with binary digit coefficients can be obtained. This arithmetic can reduce the complexity greatly.3. EBFB was a new class of even-length biorthorgonal wavelet filter banks base on Parametric Bernstein. Due to the uncertainty of parameters of the Bernstein Polynomial, a design method for optimizing EBFB filter banks based on genetic algorithms was presented. The experimental result shows that the new filter banks have better amplitude-frequency characteristic.4. To obtain the best wavelet transform of a given signal, the paper propose a method which choose the ratio energy of low-frequency domain to total signal as objective function to optimize the uncertain parameters in filter coefficients based on rationalizing the coefficients of popular biorthogonal wavelet filters and the criterion that maximizing the projection of a signal onto the scale subspace. Then we can get amatching wavelet filter which is suitable in signal compression. Correspondingly, we have given the concrete example.We used MATLAB7.0 as the simulation platform, apply the wavelet filter above in the compression of signal and image, confirm and analyze the obtained fine characteristic of wavelet filter banks.