The Study Of The Method Based On Wavelets In Signal Denoising

Signal and information processing is one of the most rapidly developed subject in the field of information science in recent twenty years. The signal processing mainly included signal denoising, character abstracting and border abstracting. Signal denoising is to be the most common in the signal processing, the classical signal denoising method such as the pure time domain method, the pure frequency region method, fourier transform method, the window fourier transform method. But these methods all have limitation in the real application. The wavelet transform is a new development unite time domain with frequency region analysis method in 1980's. And it all has well localization characteristic property in time domain and frequency region. The wavelet transform has got broad application in signal denoising. With the development of theory in wavelet, the thought of the wavelet packet transform has appeared. The wavelet packet transform is more meticulous than the wavelet transform in analyzing signal unite time domain with frequency region. The method of signal denoising in wavelet packet transform is a hot spot problem in the study of science.This paper does deeply analysis and research on the method of signal denoising based on wavelets, two new threshold value functions are structured. The main research is the method of signal denoising in wavelets based on threshold value. The main work is as the following:First of all, in the text the basic theory of fourier transform, windows fourier transform, wavelets transform and wavelet packet transform is introduced. The respective characteristic of fourier transform, windows fourier transform, wavelets transform and wavelet packet transform is analyzed and the basic theory of the multi-resolution analysis and two scales equation besides mallat algorithm based on the orthogonal wavelet transform are elaborated. In addition, some wavelet functions commonly used in the actual project question are introduced, and some questions for example wavelet packet spatial decomposition and the choice of the most best wavelet packet bases are discussed. Secondly, in above theory of wavelet foundation, from the method of low pass filter signal denoising based on fourier transform and the method of autocorrelation signal denoising, the method of threshold value signal denoising based on wavelets transform and wavelet packet transform is discussed. Besides, the method of signal denoising based on wavelet mold maximum value and the most best wavelet packet bases is introduced.At last, in this paper in analyzing the classic method of the soft threshold value signal denoising and hard threshold value signal denoising deficiency foundation, the choice of threshold value and thresholding function in threshold value signal denoising based on wavelets transform and wavelet packet transform is discussed, two new thresholding functions are structured, the numerical value experiment in the new thresholding functions by computer simulation are carried out, the effect of signal denoising with different threshold value and thresholding function are compared.