Hilbert-Huang 变换中的理论研究

1996年，Norden E.Huang等人提出了一种新的非平衡信号的时频分析方法－Hilbert-Huang变换（HHT）。它以瞬时频率为基本量，以固有模态信号为基本信号，与以往的时频分析方法相比有明显的区别，在应用中已表现出了独特的优点，但这一新方法还处在发展阶段，在建立严密的理论和方法的完善方面还有许多事要做。本文首先对这一方法作了简单介绍；然后借助振动信号模型提出了固有模态信号应满足的一个重要数学条件，进而建立了固有模态信号的数学模型，基于这一模型，论证了固有模态信号对局部对称性要求的必要性，以及用极值点拟合固有模态信号包络线和经验模态分解的合理性，这些工作使Hibert-Huang变换的研究向前迈进了一步。

Study on the Theory of Hilbert-Huang Transform

A new method to analyze time_frequency characteristics of a non_stationary signal--Hilbert_Huang transform(HHT)was developed by Norden E.Huang et al in 1996.There are obvious difference between it and other time_frequency analysis methods,since it regards instantaneous frequency as basic parameter and intrinsic mode signal as basic signal.Its particular merits have appeared in the applications.However,this method is still at seedtime and there are many things to do in founding its rigorous theory and perfect procedure.In the paper,the new method is briefly introduced,and the model of vibration signal is presented to develop an important mathematics condition that the intrinsic mode signal shoul satisfy and then to esablish the mathematics model of the intrinsic mode signal.Based on this mathematics model,the necessarity of the local symmetry of an intrinsic mode signal is deeply demonstrated and the rationality of fitting the envelops of an intrinsic mode signal by its extrema and decomposing signal with the empirical mode decomposition is illustrated.The above work pushes the researche on the HHT with a further advanced step.