6 The Differences Analysis on Filtering Properties of Wavelet Decomposition and Empirical Mode Decomposition

Wavelet Decomposition (WD) and Empirical Mode Decomposition (EMD) are working differently to the filtering properties of non-stationary signals. In order to better understand the differences, their practical effects, advantages and disadvantages, this paper proposes an approach to compare the differences of filtering properties between WD and EMD by using the weight average power spectrum analysis of Gaussian white noise signal. Also, this paper proves the validity of the proposed methods. The experimental results indicate that the methods proposed by this paper can effectively explain the filtering properties of these two decompositions. To EMD, each component weight average power spectrum shows a group of ordered band pass filter in which the bandwidth decreases and the center frequency reduces gradually. The whole decomposition process is automatic but with edge effect which could influence the decomposition quality; to WD, it demonstrate distinct wavelet bases, some show the same multi-scale filtering properties as EMD while the other are distinct, or even completely distinct. Therefore, selecting different wavelets and setting different number of decomposition layers will probably lead to quite different decomposition consequences. The whole process of WD is very fast. Its mean time is only 1/25 of EMD. But it depends on how to select wavelet basis.