The Wavelet-based Denoising Methods And Its Applications In Signal Processing Research

With the maturation and development of the methodology, signal processing has become an important tool in modern science technology, and it is widely used in voice, image, communications, machinery and other fields. Wavelelt analysis is an emerging discipline which is developing rapidly in signal processing field. It is an analytical tool which based on the Fourier analysis, and has a broad application background. In signal processing, complex background noise usually exists in the data collected and it is difficult to filrer out background noise. Wavelet transform has a flexible variable time-frequency window, has can effectively extract useful information from the signal. Therefore, it is the concern of scholars home and abroad in signal processing field. At present, the research and application of the wavelet denoising method are still more space for development. We have proposed some improved denoising method on the basis of traditional denoising method.In this dissertation, we have proposed a critical-thresholding denoising based on the theory of hard-thresholding and soft-thresholding method. The critical-thresholding denoising method can not only overcome the disadvantage of the constant deviation with the original signal cause by soft-thesholding method, but also make up for the deficiency of hard-thresholding not entirely removing noise.In traditional wavelet coefficients correlation denoising method, the wavelet coefficients of each scale will have little offset after the wavelet transform to the noisy signal. For this problem, we have proposed a wavelet coefficients correlation denoising method based on cross-correlation function. Cross-correlation algorithm is used to calculate the offset between each scale coefficient and original noisy fault signal. Then do correlation analysis to the shift scale signal so as to get accurate mutation signal.Due to the fact that it is not easy to filter out the overlap noise between noisy signal and noise using the traditional method of wavelet denoising, an adaptive filter model based on the wavelet transform is constructed. In this model, the adaptive filter is used to filter out noise secondary on the basis of first wavelet denoising on the original noisy signal. After the iteration with the adaptive filtering algorithm, the filter output is the denoised signal. In the adaptive filter model based on the wavelet transform, we apply Hopfield neural network to realize adaptive filtering LMS algorithm, improving the cspeed of operation.Aiming at the issue of the traditional stochastic resonance only applicable to deal with low-frequency signals, a high-frequency weak signal detection method based on stochastic resonance is proposed. By analyzing the relationship among the traditional stochastic resonance model parameters, the input signal amplitude, the noisy signal and the signal to noise ratio of output, an additional gain is added to the original model which makes the sampling time multiplied reduced in the stochastic resonance system, in order to achieve the mapping from high-frequency signal to low-frequency signal.As the stochastic resonance is only applicable to solve the issue of single-frequency signals, a multi-frequency stochastic resonance detection method based on wavelet transform in weak signal is proposed. Do the first wavelet transform to multi-frequency weak noisy signal to realize the separation of the various frequency bands, and then select the detail signal and approximation signal of each layer signal as the input signal of stochastic resonance, so as to realize the detection of multi-frequency weak signal.These denoising methods have applied to several different actual backgrounds, the simulation results show that the application of these denoising methods can achieve good denoising effect.