Detrended Fluctuation Analysis For Empirical Mode Decomposition Based Denoising

Abstract

Empirical mode decomposition (EMD) is a recently proposed method to analyze non-linear and non-stationary time series by decomposing them into intrinsic mode functions (IMFs). One of the most popular application of such a method is noise elimination. EMD based denoising methods require a robust threshold to determine which IMFs are noise related components. In this study, detrended fluctuation analysis (DFA) is suggested to obtain such a threshold. The scaling exponential obtained by the root mean squared fluctuation is capable of distinguishing uncorrelated white Gaussian noise and anti-correlated signals. Therefore, in our method the slope of the scaling exponent is used as the threshold for EMD based denoising. IMFs with lower slope than the threshold are assumed to be noisy oscillations and excluded in the reconstruction step. The proposed method is tested on various signal to noise ratios (SNR) to show its denoising performance and reliability compared to several other methods.