The Application Of Wavelet Analysis In One-Dimensional Signal De-Noising

The widespread noise makes signal de-noising a hot topic in the field of signal processing. The signal with noise is bad for the transmission, receiving, analysis, processing etc., thus it is necessary and important to remove or diminish noise to extract useful signal during signal pre-processing.The traditional ways for signal denoising are pure time-domain method, pure frequency-domain method and so on, but there are many disadvantages that are difficult to overcome for these ways. Recently, wavelet analysis has developed quickly and became a new way for signal denoising because of good localization characterization in time-domain and frequency-domain. It is widely used in the area of signal processing and is a hot issue for research.There are kinds of ways for signal denoising through using wavelet analysis, such as wavelet package, wavelet threshold, modulus-maximum denoising and so on. Based on the theory of wavelet decomposition and reconstruction, multi-resolution analysis and the construction of wavelet bases, this paper states the feasibility of wavelet threshold denoising. During the process of wavelet threshold denoising, the key step is to select the threshold function. The good threshold function can remove the noise effectively. Through comparing the denoising effect of hard threshold, soft threshold and compromised threshold function, the improved threshold function is proposed. The simulation results of every kind of threshold function show that the denoising performance of the improved threshold function is much better than other threshold functions. The second research content of this paper is denoising for signal by using wavelet transform modulus maximum. In this paper, UWB (Ultra-Wide Band) signal is set as an example to state the principle and method of de-noising. In order to eliminate the noise effectively, two points were improved as the following. First one is Adaptive threshold algorithm was applied to process the modulus maxima at the maximum scale level. Secondly, The modulus maxima of the first scale level which had obvious influence for the reconstructed signal were calculated by nonlinear least square method. The simulation results show that the improved method can remove the noise and reconstruct the signal better compared with the traditional algorithm.