The Method Of Eliminating Gibbs Phenomenon In Wavelet And Multiwavelet Transform And Its Application

Nothing is more important than the signal filtering processing in the modern signal processing. The most useful tools in the signal processing are time-frequency analysis method. Now, the common time-frequency analysis method is Fourier analysis, wavelet analysis and so on. All these methods almost have the same defect when they are used for filtering. The defect is called the Gibbs phenomenon.Gibbs phenomenon is a universal problem in the signal processing. Now the academes have no idea about the solution of the Gibbs phenomenon. According to the theory study, this paper discusses and analyzes the reason of the production of Gibbs phenomenon systematically. In this paper, the Gibbs phenomenon in wavelet and multi-wavelet which is very popular in the signal processing is discussed in detail, and the improvement of the eliminating Gibbs phenomenon simulation is studied very much. Some experienced inclusion is got in the simulation, and some of them can be explanation in the theory.This paper is set about with simple wavelet threshold method firstly, then it analyzes all kinds of threshold method character. The more effective threshold is chosen. After analyzing the defects of the soft/hard threshold, a new threshold between the soft/hard thresholds is used to take place them. The popular circle-spinning method is used to improve the Gibbs phenomenon, and integrated with the new threshold.The multi-wavelets have some super advantages than traditional wavelets. In this paper, the elementary research of the multi-wavelet de-noising method is done first time in our motherland. For there is no better multi-wavelets toolkit, the multi-wavelet arithmetic is carryed out with the m-file of MATLAB in this process. And, like the traditional wavelet, the MATLAB programs are used in the multi-wavelet de-noising process. The simulation results prove that the elimination of Gibbs phenomenon still have a lot of work to be done.