A novel denoising method for non-linear and non-stationary signals

Signal denoising is a crucial step in signal analysis. Various procedures have been attempted by researchers to remove the noise while preserving the effective components of the signal. One of the most successful denoising methods currently in use is the variational mode decomposition (VMD). Unfortunately, the effectiveness of VMD depends on the appropriate selection of the decomposition level and the effective modes to be reconstructed, and, like many other traditional denoising methods, it is often ineffective when the signal is non-linear and non-stationary. In view of these problems, this study proposes a new denoising method that consists of three steps. First, an improved VMD method is used to decompose the original signal into an optimal number of intrinsic mode functions (IMFs). Second, the energy variation ratio function is applied to distinguish between the effective and non-effective IMFs. Third, the valuable components are retained while the useless ones are removed, and the denoised signal is obtained by reconstructing the useful IMFs. Simulations and experiments on various noisy non-linear and non-stationary signals demonstrated the superior performance of the proposed method over existing denoising approaches.