HHT的理论依据探讨——Hilbert变换的局部乘积定理

LOCAL PRODUCT THEOREM OF HIBERT TRANSFORM-THEORETICAL BASE OF HHT

希尔伯特-黄变换(Hilbert-Huang Transform,简称HHT)是上世纪90年末才出现的一种非平稳信号分析方法,对于这种方法的理论框架还有值得深入探讨的空间。为了进一步,探索HHT的理论依据,本文从分析HHT的固有模态函数(Intrinsic Mode Function,简称IMF)的定义入手,在Hilbert变换的Bedrosian乘积定理基础上提出了Hilbert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巧妙地论证了这一定理,从而首次为HHT中IMF的定义、瞬时频率的计算公式、经验模态分解(Empirical Mode Docomposition,简称EMD)及其收敛性等系列问题提供了较统一的理论依据。

As the theoritical base of a new method for analyzing non-stationary signal, Hilbert Huang transform (HHT), starting from analzing the definition of Intrinsic Mode Function (IMF), is introduced and a local product theorem of Hilbert Transform is developped on the base of Bedrosian product theorem. The theorem is proved by the way of combining theoritical derivation and physical meaning analysis. Thus, the common theoritical base of some contents of HHT such as the definition of IMF, the formula for calculating instantaneous frequency, Empirical Mode Decomposition (EMD) and its convergence property, and so on are provided.