The Structure And Application Of Adaptive Wavelet

From the perspective of signal processing, In the characterization of information, FT can clearly reveal the characteristic of signal in the frequency domain,But at the same time the defect is not reflected the local information in the time domain.In order to overcome the limitations of FT, People have carried on the promotion and putted forward a lot of signal analysis method, such as WFT, Gabor transform and wavelet transform,Which wavelet transform is the most far-reaching impact in many ways. Because the wavelet transform has the time-frequency localization and multi-resolution analysis, To detect the normal signal transient and demonstrate its frequency components, So it is widely applied to various of time-frequency analysis field, especially suitable for non-stationary signal processing.In the field of signal processing, because of wavelet transform has the flexibility in the selection of wavelet base, so an important problem of wavelet analysis is the selection of wavelet base.The existing selection method which based on available wavelet has been constructed for specific issues, according to specific criterion or practice experience, to select a relatively good wavelet basis. However this method is usually restricted by existing wavelet,To avoid this restriction, The method which matching the corresponding wavelet by the given signal becomes an option.If this idea is Feasible, and then we can analyze the given signal with matching wavelet. On the one hand, it can overcome the problem of the selection of wavelet base.on the other hand, from the given signal to match wavelet, then the signal analysis results can be better response signal characteristic.This article is mainly based on the method and algorithm of Chapa and Rao about from a given signal matching with limited orthogonal wavelet, we do further improvements.The improved method has overcome defect of the method of Chapa and Rao. at the same time we gives the improved algorithm. Compared to the former method, one of great advantages of the improved algorithm is simplicity in calculation. In addition, In the matching process,The amplitude spectrum and phase spectrum of scaling function were not calculated respectively. based on the work of Gupta, Joshi and Prasad and biororthogonal perfect reconstruction filter banks theory, by using Chapa and Rao hypothesis,We reconsider the problems that signal of the scale space and the next level of scale space difference energy minimization. and then obtained matching biororthogonal compactly supported wavelet method by the test signal, in the meantime, we gives the realization of the algorithm. The algorithm can match biorthogonal compactly supported wavelets by the given signal. Finally, in order to test the two algorithm is correct and effective,We apply those algorithm to one-dimensional and two-dimensional signals processing, the simulation results indicates that, According to the matching wavelet function and scaling function for a given signal, and to achieve preferably real-time signal processing.In addition, we combine Peng Lizhong’s beautiful wavelet system with the improved Chapa and Rao matching method, We derived a method of self-adaptive beautiful wavelet by the given signal. The algorithm can get4band beautiful wavelet by the given signal, It can decompose the test signal into4different frequency components.