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

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.