Local wave decomposition based on lifting wavelet denoising and its application

Aiming at the mode mixture caused by the noise in LWD (local wave decomposition), a novel method combining LWD and lifting wavelet denoising is proposed. we present a lifting scheme to construct adaptive wavelets by the design of prediction operator and update operator. According to the local characteristics of signal and the selection criterion of minimizing the squared error, an optimal predicting operator is selected for a transforming sample so that the lifting wavelet basis function can always fit the local characteristics of the signal. The original signal is preprocessed using the lifting wavelet to suppress abnormal interference of noise, reduce the mode mixture, and improve the quality of decomposition. Furthermore, integration of LWD with Hilbert envelope analysis is conducted. Experimental analysis results show that the proposed method can be used to avoid the mode mixture effectively and is specially reasonable and suitable for analyzing nonlinear and nonstationary signals.