The empirical optimal envelope and its application to local mean decomposition.

Envelopes, which represent the overall information of the signal amplitude variation, are the necessary mediums in many signal decomposition methods. The phenomena of undershoot and overshoot result in the error of envelope estimation and unexpected signal decomposition components. In this paper, an accurate envelope estimation method, called the empirical optimal envelope (EOE), is proposed and applied to the local mean decomposition (LMD). First, an indicator of envelope distance is defined to describe the features of the ideal envelope. Utilizing the indicator, an iterative algorithm for the approximation of tangency points is designed. The tangency points, instead of the extreme points, are interpolated to realize the EOE. Then, the EOE is integrated with the LMD, and two interpolation functions, the cubic spline and the piecewise cubic Hermite interpolating polynomial, are combined to improve the efficiency and convergence of signal decomposition. Finally, the proposed method is verified by simulated signals and actual signals.