Extraction Of Signal Using Wavelet Transform Under The Strong Noise Background

Abstract In actual gathering signal process, because of the data acquisition environment and the instrument measuring of completing the data acquisition task, there are disturbances and the noise of other signals inevitably. The noise existence has the disadvantageous influence in scientific research and the production work after the data acquisition and the signal survey. These noise signals will cover the useful signal which we will need. Therefore, in order to eliminate noise signal and effectively display the useful information of the primary signal, it is essential to process the actual gathered signal. The effect directly affects following work based on signal analysis, diagnosis, recognition. In order to enhance the technical specification and withdraw the accurate signal, removing the unwanted signal and the stochastic noise signal should count for much. Because the wavelet transform has characteristic of the low entropy, the multi-resolution, the de-relevance and choosing the base nimbly, it becomes the synthesis of the characteristic withdrawing and the low pass filter function, namely, it is equal to simultaneously carrying on the filter of the low pass and high pass to the signal. Its low frequency coefficient mainly reflects signal information, but high frequency coefficient mainly reflects noise and signal detail information. Wavelet transform has the quite big superiority in the signal processing, and the incomparable superiority in particular to non- steady signal processing for Fourier transform.In detail, this article mainly develops the following several aspects:1. Second chapter contrasts merits and shortcoming of Elimination noise using the wavelet transform and the traditional filter. Regarding wavelet transformation, it has partial characteristic in the time domain and the frequency range, and has still the multi-resolution characteristic. So it adapts to analyzing the signal simultaneously having low frequency and high frequency. Besides, based on wavelet coefficient difference along with scale change after signal and noise transformation, this article proposes the denoising method based on the wavelet transform.2. In many practical application situations, signal is nonsteady, and its statistic (for example correlation function, power spectrum and so on) is time-changing function. Only understanding the signal over-all characteristic in the time domain or the frequency range is by far insufficient, and we hope to obtain the signal frequency spectrum along with time change. For this, we need the time and the frequency union function which expresses signal. This kind of expression is called the time frequency distribution of the signal. This article mainly introduces short-time Fourier transform, Gabor transform and wavelet transform.3. Introducing the wavelet denoising theory, this article has made the analysis to its correlation parameter. Based on correlation function, and following the principle which the wavelet base selects, five kinds of wavelet base functions are compared. According as correlation coefficient which estimates signal processing effect, and after five kind of commonly used wavelet base functions selecting different parameters, The decomposed, renewably constructed signal and the primary signal have carried on the comparison. Based oncorrelation coefficient value, the best wavelet base function is chosen. Conclusion is educed: In view of pulse signal, and Based on Daubechies wavelet, the effect is better using discrete binary system wavelet transform.4. Because of pulse signal probability density sparse characteristic, the existing wavelet thresholding denoising effect is not obvious. This article compares the pulse signal probability density with the sparse distribution probability density function, and brings forward Maximum likelihood estimation thresholding denoising. First, denoise for noise signal of known primary signal, and compare with original soft hard thresholding denoising, using correlation function. Next, in view of noise signal which haven't primary signal, estimate several parameters in the threshold value formula, then carry on denoising, and compare with original effect. The research indicates: In view of pulse signal, using wavelet transform and choosing maximum likelihood estimation thresholding method, the effect surpasses traditional wavelet denoising. Thus, for the launched pulse signal, This method provides the certain application value in order to withdraw the useful signal.