A Minimum Arclength Method for Removing Spikes in Empirical Mode Decomposition

Empirical mode decomposition (EMD) is an extensively utilized tool in a time-frequency analysis. However, disturbances, such as impulse noise, can result in a mode-splitting effect, in which one physically meaningful component is split into two or more intrinsic mode functions (IMFs). In this paper, we propose a novel method, minimum arclength EMD (MA-EMD), to robustly decompose time series data with impulse-like noises. The idea is to apply a minimum arclength criterion to adjust the knot positions of impulses during the sifting process in EMD. In this way, the impulse-like artifact is extracted with the first IMF, and the mode splitting effect of the latter decomposition is alleviated. Furthermore, when the first IMF contains the desired information, we separate the spikes and the first IMF by adding a pair of masking signals. For using this masking-aided MA-EMD (MAMA-EMD) method, we also mathematically derived the appropriate ranges of the frequency and the amplitude of the masking signal. The MAMA-EMD is utilized to deal with the simulated Duffing wave and four real-world data, including electrical current, vibration signals, the cyclic alternating pattern in sleep EEG (electroencephalography), and circadian of core body temperature. The results show that the MA-EMD and MAMA-EMD have a sound improvement when encountering impulse noises.