An improved EMD method with modified envelope algorithm based on C2 piecewise rational cubic spline interpolation for EMI signal decomposition

In this paper, we propose an improved empirical mode decomposition (EMD) method, termed IEMD, with modified envelope algorithm based on C2 piecewise rational and C2 monotone piecewise rational cubic spline interpolations, for the decomposition of nonlinear and non-stationary EMI signals. In the sifting procedure, we first construct the upper and lower envelopes employing C2 piecewise rational cubic spline interpolation (PRCSI) technique. Considering the existence of undershoots, we further modify the original envelopes iteratively with C2 monotone piecewise rational cubic spline interpolation (MPRCSI) technique, for the elimination of undershoots as accurate as possible. Experiments on synthetic and real signals, compared with three improved versions of EMD, three for ensemble EMD (EEMD) and TL-SVD, demonstrate that the proposed method is more valid and flexible when applied to the decomposition of synthesis harmonic signals and real EEG signals, signifying it also can be applied to the decomposition of EMI signals which are known to be extremely nonlinear and non-stationary.