Empirical numerical study on denoising by wavelet and by second kind of fourier analysis

Abstract

As the wavelet bases usually have relative small support sets, three defects of wavelet denoising for a complex time series can be deduced. The first defect is that for in large sample size, the wavelet denoising is not better than the second kind, Fourier analysis denoising. The second is that wavelet denoising has the worse reconstructive capacity for the high frequency signal. The last defect is that the wavelet denoising is not better when there are many outliers. The numerical experiments are carried out to make sure the three deductions.

Application of Wavelet De-Noising in Non-Stationary Signal Analysis Based on the Parameter Optimization of Improved Threshold Function

“…In the electro-mechanical system, most of the signals are non-stationary. According to the multi-resolution and self-similarity of wavelet analysis, Non-stationary signal can be accomplished by eliminating the added white noise [1][2][3][4][5]. Among all the de-noising methods on account of wavelet analysis, the threshold value method proposed by Donoho [6] is more simple and effective, this method takes the corresponding signal wavelet coefficients who have bigger amplitudes and less quantity for containing important information of the signal, on the contrary, the corresponding wavelet coefficients of noise are uniformly distributed, whose number is more, but the amplitudes are small.…”