本征模式函数与自伴微分方程的关系研究

A research on intrinsic mode functions and the self-adjoint ordinary differential equations

本征模式函数(IMF)是Huang在经验模式分解(EMD)算法中定义的一类函数.根据IMF的定义与自伴常微分方程解的特点之间的相似性,研究了二者之间的关系,得出了本征模式函数是某个自伴二阶常微分方程的解这一结论,并借鉴前人的分析方法给出了证明.

Intrinsic mode functions （IMF） are a class of functions defined by Huang in the empirical mode decomposition （EMD） algorithm. According to the similarity between IMF and the solutions of self-adjoint ordinary differential equations （ODEs）, the relationship between them is studied and a theorem that the IMF decomposed by EMD is a solution of the self-adjoint ODE is obtained. With drawing on the analysis method of predecessors, the proof of this theorem is given.