Application of wavelet analysis for denoising

Wavelet transform has not only the character of Fourier transform and inversion, but also the character of the time-frequency window. Wavelet transform is an approach that the time-frequency window area is fixed but its shape can be adjusted. It can be well localized in both time and frequency domains. It consists a flexible time-frequency window. For low frequency, it has high frequency resolution and low time resolution, and for high frequency, it has high time resolution and low frequency resolution. So the wavelet analysis has more quality than Fourier analysis in signal processing. The wavelet has multiresolution ability, we can use the Mallat algorithm to decompose and reconstruct the signal. Wavelet transform has been applied in many fields such as the strange point examination, image processing, the signal filtering, and denoising. In this paper, the application of wavelet analysis in denoising is presented, we can see that it both degrades the noise of smooth and rough signals, it is superior than Fourier analysis.