希尔伯特-黄变换的统一理论依据研究

RESEARCH ON THE UNIFORM THEORETICAL BASIS FOR HILBERT-HUANG TRANSFORM(HHT)

希尔伯特-黄变换(HHT)是上世纪末出现的一种分析非线性、非平稳信号的有效新方法,但其理论依据还不太明朗,尤其缺乏统一理论依据。从分析HHT的基本模式函数(IMF)定义入手,在H ilbert变换的Bedrosian乘积定理基础上提出了H ilbert变换的局部乘积定理,采用理论推导和物理意义分析相结合的方法对其进行了论证。然后应用这一定理对HHT中的IMF定义、瞬时频率计算公式、经验模式分解(EMD)方法及其收敛性等问题给出了统一解释,从而初步为HHT提供了一个统一理论依据。

Hilbert Huang transform(HHT) is a new effective method developed at the end of last century for analyzing nonlinear and non-statgionary signal.However,its theoretical basis is not clear until now,especially it is short of its uniform theoretical basis.Starting from analyzing the definition of Intrinsic Mode Function(IMF)of HHT,this paper presents a local product theorem of Hilbert Transform based on its Bedrosian product theorem.The theorem is proved in the way of combining theoretica deduction and physical meaning analysis.Some problems such as the definition of IMF,the formula for calculating instantaneous frequency,Method of Empircal Mode Decomposition(EMD) and its convergence property are congruously explained by this theorem.Thus a primary uniform theoretical basis is provided for HHT.