An Improved Empirical Wavelet Transform for Noisy and Non-Stationary Signal Processing

Empirical wavelet transform (EWT) has become an effective tool for signal processing. However, its sensitivity to noise may bring side effects on the analysis of some noisy and non-stationary signals, especially for the signal which contains the close frequency components. In this paper, an improved empirical wavelet transform is proposed. This method combines the advantages of piecewise cubic Hermite interpolating polynomial (PCHIP) and the EWT, and is named PCHIP-EWT. The main idea of the proposed method is to select useful sub-bands from the spectrum envelope. The proposed method selects the maximum points of the spectrum to reconstruct the spectrum envelope on the basis of PCHIP. Then, a new concept and a threshold named the Local Power (LP) and lambda are defined. Based on the new concept LP and the lambda, the useful sub-bands can be obtained. Finally, the experimental results demonstrate that the PCHIP-EWT is effective in analyzing noise and non-stationary signals, especially those that contain the closely-spaced frequencies.