The Application Of Wavelet Analysis In Signal De-noising

Wavelet analysis is one of the most rapidly developed subject in recent years, it iswidely used in signal processing and image processing. In signal processing, signalde-noising is most common case and the classical de-noising methods such as puretime-domain method, pure frequency-domain method, the fourier transform method, thewindow fourier transform. But they have limitations in their application. Waveletanalysis is a new de-noising method,it can analyze signals in time domain andfrequency domain. It has a local nature,so it is widely used in some fields. In the1995,Donoho and Johnstone put forword hard and soft thresholding function method.Both of them have better de-noising effect,but their also have their own defects. Hardthresholding function method handling the signal has a larger variance in de-noisingresults and soft thresholding function method has a smooth results,but it reduces andretains all the wavelet coefficients which is greater than the wavelet coefficients of thethreshod and make the results have a large deviation. Based on this, an improvedthresholding function is proposed in this paper. this function is continuous. Thede-noising effect of the method is obvious, and the SNR is greatly improved. Details areas follows:Basic theories of wavelet analysis in this paper are introduced detailed, brieflyfrom the traditional Fourier analysis, through the development of the window Fouriertransform, and then the wavelet transform is appeared; The core part of the waveletanalysis are introduced—Multiresolution analysis, Mallat decomposition reconstructionalgorithm and wavelet packet. Several common wavelet and mathematical conceptsabout the wavelet nature are introduced briefly.Wavelet thresholding de-noising method are researched and studied in this paper，including the basic theory of wavelet thresholding de-noising, the selecting of thewavelet basis, thresholding value and thresholding function. Base on the basic theoriesof signal de-noising and traditional thresholding function, Then an improvedthresholding function is proposed. This method overcomes the defects of the traditional thresholding function. Through the simulation experiments, the de-noising effect of theproposed thresholding method is better than hard and soft thresholding method andGarrote thresholding function method.