HHT经验模式分解的周期延拓方法

A Periodic Extension Approach for HHT Empirical Mode Decomposition

针对经验模式分解的端点效应,运用插值理论,给出了端点邻域处三次样条插值引起的截断误差表达式,分析了产生端点效应的原因,提出采用对称(镜像)和反对称两种信号周期延拓的方法。为保证周期延拓的平滑性,对于端点为极值点或零点的不同情况,提出了分别采用对称(镜像)和反对称周期延拓的方法。通过对截断误差的分析,以及对典型模拟信号和语音实验数据的计算,证明了周期延拓方法的有效性可行性,方法可以大大地提高经验模式分解的准确性和可靠性。

To overcome the boundary effect of empirical mode decomposition, the truncation error of cubic spline interpolation in the endpoint neighborhood is described by using the theory of interpolation. The causation of the boundary effect is analysed. The periodic extension approach is developed in this work. To guarantee the smoothness of the periodically extended signal, both the symmetric and anti - symmetric extensions are proposed. The former, also referred to as mirror extension, can be applied to the case when the signal reaches its extreme at the ends, while the latter is designed for the case where the signal takes zero values. The truncation error and the success of applying both extensions to some typical simulating signals and speech data demonstrate the validity and feasibility of this method, and hence greatly improving the precision and reliability of the decomposition.