Research On Signal Singularity And Denoising Based On Matching Wavelet Transform

Wavelet transform as a new signal processing method, because it is both in time domain and frequency domain has the ability of denoting local signal information, so the wavelet transform has been widely used in the Modern Signal Processing.In engineering application,one of the most important issues of wavelet analysis is the selection of the wavelet function. This is because the wavelet functions in wavelet transform have the diversity, and even some wavelet functions have no fixed expressions.In addition, using different wavelet functions with different characteristics to analyse the same problem,different results often can be got. However, for a signal, how to choose a suitable wavelet function to analyse and deal with, has not a unified standard.This paper examines a large number of information and documentation at home and broad, in-depth studys the basic theoretical knowledge of wavelet analysis and multi-samping filter banks, and around the application of matched wavelet starts certain research and analysis.Firstly, based on wavelet analysis and signal singularity detection, this paper researches a preferred method of the matched wavelet which matches with a given singular signal. Depending on the characteristics of the singular signal, and considering synthetically the compact support, regularity and vanishing moments, they restrict each other, the matched wavelet function is perfectly selected, and by simulation to verify the effectiveness of the method.Secondly, based on wavelet analysis and signal de-noising analysis, this paper researches a construction method of wavelet function which matches with a given one-dimension signal depended on filter bank. According to the characteristics of the given signal,by introducing a variable parameters in order to design the wavelet filter bank and the matched wavelet,and discusses the application of the matched wavelet in the signal decomposition and reconstruction as well as the signal de-noising. Compared with the existing classic wavelet function, to verify the validity of the method.