傅里葉變換與小波變換在信號去噪中的應用

　　對于高頻信號和高頻噪聲干擾相混疊的信號，采用小波變換去除噪聲可以避免用傅里葉變換去噪帶來的信號折損。對于噪聲頻率固定的平穩信號，在對信號進行傅里葉變換后使用濾波器濾除噪聲。對高頻含噪信號則采用正交小波函數sym4對信號分解到第4層，利用極大極小值原則選擇合適的閾值進行軟閾值處理，最后利用處理后的小波系數進行重構。實驗結果表明，對于高頻含噪信號傅里葉去噪會出現嚴重的信號丟失現象，使用極大極小值原則選擇閾值進行小波去噪可以有效地保留高頻部分的有用信號。

　　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.