An improved EMD based on cubic spline interpolation of extremum centers

Classical cubic spline interpolation is prone to overshoot and undershoot when used to interpolate the envelopes during Empirical Mode Decomposition (EMD). A new method is proposed to envelope the signal and to get the potential Intrinsic Mode Function (IMF) components, which is called Extremum Center Interpolation (ECI). In ECI, all the extrema will be connected with segments to form the envelope area and the centers of it called extremum centers will be obtained. The potential IMF component will be gotten by interpolating the extremum centers with cubic spline interpolation. When used to decompose signals whose extrema are unevenly distributed, whether it is simulation signal or real hydraulic shock signal, the newly proposed EMD will have a significant advantage over the original EMD. To evaluate the overshoot degree of the envelopes and to decide whether to use the newly proposed EMD or the original one to decompose the goal signal, an index called overshoot index is proposed and its threshold is obtained by numerical experiments.

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