Improving empirical mode decomposition with cubic smoothing spline fitting

Pseudo intrinsic mode often appears in the process of empirical mode decomposition (EMD) and negative instantaneous frequencies are also induced into the succeeding Hilbert-Huang Transform (HHT). We aim to find what causes the appearance of these phenomena and then to propose a method for improving EMD, which can suppress these phenomena. In the full paper, we explain what we do in some detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: the effect of sampling rate on EMD results. Its two subtopics are: the effect of signal sampling rate on EMD and HHT transform (subtopic1.1) and the analysis of reasons for the negative instantaneous frequencies in HHT spectra (subtopic1.2). In subtopic 1.2, we explain that the negative instantaneous frequencies are caused by pseudo intrinsic modes because the signal sampling rate is too low. Thus a criterion to judge the pseudo intrinsic mode of EMD is proposed that, if the HHT spectrum is not stable or negative frequency appears, the corresponding mode is a pseudo intrinsic mode. The second topic is: the improvement of EMD through fitting with cubic smoothing spline. In this topic, we use the cubic smoothing spline fitting to interpolate and reconstruct the original signals to increase the nominal signal sampling rate. Also in this topic, numerical simulation results, given in Figs.6 and 7 in the full paper, show preliminarily that the improved EMD can effectively avoid the distortion of the envelope curve induced by low sampling rate, thus eliminating pseudo intrinsic modes in EMD and negative instantaneous frequencies in HHT.