傅里叶变换与小波变换在信号去噪中的应用

　　对于高频信号和高频噪声干扰相混叠的信号，采用小波变换去除噪声可以避免用傅里叶变换去噪带来的信号折损。对于噪声频率固定的平稳信号，在对信号进行傅里叶变换后使用滤波器滤除噪声。对高频含噪信号则采用正交小波函数sym4对信号分解到第4层，利用极大极小值原则选择合适的阈值进行软阈值处理，最后利用处理后的小波系数进行重构。实验结果表明，对于高频含噪信号傅里叶去噪会出现严重的信号丢失现象，使用极大极小值原则选择阈值进行小波去噪可以有效地保留高频部分的有用信号。

　　Abstract:

　　For high frequency signals mixed with high frequency noise， using wavelet to de-noise can avoid the useful signal impairment caused by Fourier transform. For a fixed frequency noise signal， using Fourier transform and low filter to reject the noise. For a mixed high frequency noise signal， it is more effective to use orthogonal wavelet function sym4 to de-noise. It firstly decomposite the signal to the fourth floor，and select the appropriate number for soft threshold by minimax criteria. Finally， it use the threshold number to select effective wavelet coefficients for reconstructing the de-noised signal. Experimental results show that such a noisy signal can lost some useful info by Fourier de-noising， and by using the minimax principle to select wavelet threshold can effectively keep some of the useful signal， especially the high-frequency part.