An Investigation Study on Mode Mixing Separation in Empirical Mode Decomposition

Abstract

Mode mixing is a limitation of the empirical mode decomposition (EMD) method appropriate for physiological signal analysis. In 2008, boundary condition map presented by Rilling and Flandrin provided the efficiency of separating the two components of a two-tone signal as a function of their amplitude and frequency ratios. Until 2019, their findings were still applied. However, their maps only give an uncertainty-like efficiency of mode mixing separation for two-tone signals. In this paper, we propose a criterion for mode mixing separation in EMD, which provides a binary judgment on mode mixing separation instead of the above-mentioned efficiency. By comparing the slopes of the two components, we found that the phenomenon of mode mixing occurs as the extrema of the high-tone component are suppressed by the low-tone component. Under this condition, the criterion shows the relation among their amplitude ratio, frequency ratio, and relative phase between the two components. Given with the values of the three parameters, one can affirm whether the two components are mixed according to the criterion. Accordingly, we derive a black/white three-dimensional (3D) map that plots the binary result of mode mixing in black or white as a function of the three parameters. Our map agrees with Rilling's map and the results obtained from our gait analysis. Among the 23 sets of center-of-mass trajectory signals, six sets encountered the mode mixing problem and their coordinates of the three parameters were found in the black region of the map, while the other 17 sets were in the white region.