小波变换及其在去噪中的应用

Wavelet transform and its application to noise eliminatlon

小坡变换是一种能同时在时间（或空间）和频率域内进行局部化信号分析的新方法。其主要优点在于它在时域（空域）和频率域都有良好的局部化性质，而且由于对高频成分采用逐渐精细的时域（空域）取样步长，从而可以聚焦到信号的任意细节。原则上讲，凡是使用傅里叶变换的运算均可用小波变换代替，而且不受短时窗的局限。在本方法的实现过程中，首先构造尺度函数与小波函数，求出相应的频率响应，利用Mallat算法对信号进行塔式分解，再根据有效波与干扰波的频谱差异，区分有效信号与噪音，将噪音部分置零，最后用Mallat重建算法得到去噪后的信号。

Wavelet transform is a new method that can be used to achieve part signalanalysis simultaneously in time (or spatial) domain and frequency domain. Its majorsuperiorities lie in good part characteristics in both time (or spatial) domain andfrequency domain,as well as focusing attention to any signal details due to increas-ingly shorter time (or spatial) domain sampling step size for high frequency con-tents. In principle,any operation in which Fourier transform is performed can be re-placed by the wavelet transform,without the limitation of short time window.This method consists of the steps:(1) forming scale function and wavelet function to obtain corresponding fre-quency response;(2) making 'cone decomposition' of signals by Mallat's algorithm 3(3) telling effective signals from noises according to their spectrum difference,and;(4) zer0ing noises and acquiring signals by adopting Mallat's reconstructionalgorithm.