Hilbert‐Huang transform，一种时间尺度的寻找方法

主要内容:
前些天在973年会上宋黎明老师介绍了Hilbert-Huang变换法，简称HHT，说是类似于FFT、小波变换等方法，但最重要的是不需要基底。但也可以发现时变上的一些信息。

于是我也搜一下相关的信息。
从百度百科看到它的主要特点：1.HHT可以分析非平稳信号；2.自适应，无需预先基底（还是有本质函数的，不过是自动去找）。

宋老师当时引用的应该是这篇文章（被引771次）：http://adsabs.harvard.edu/abs/1998RSPSA.454..903E
查了一下，ADS也有好些用这个方法的，比如这篇做QPO的：http://adsabs.harvard.edu/abs/2014ApJ...788...31H
还有做太阳flare的：http://adsabs.harvard.edu/abs/2015MNRAS.451.4360K

这个方法也可以用到GRB的光变上来呀，也可以用到SwJ1644+57等类似的源上去。

精彩摘抄:
从百度百科抄下来：1998年，Norden E. Huang（黄锷：中国台湾海洋学家）等人提出了经验模态分解方法，并引入了Hilbert谱的概念和Hilbert谱分析的方法，美国国家航空和宇航局（NASA）将这一方法命名为Hilbert-Huang Transform，简称HHT，即希尔伯特-黄变换。

HHT主要内容包含两部分，第一部分为经验模态分解（Empirical Mode Decomposition，简称EMD），它是由Huang提出的；第二部分为Hilbert谱分析（Hilbert Spectrum Analysis，简称HSA）。简单说来，HHT处理非平稳信号的基本过程是：首先利用EMD方法将给定的信号分解为若干固有模态函数（以Intrinsic Mode Function或IMF表示，也称作本征模态函数），这些IMF是满足一定条件的分量；然后，对每一个IMF进行Hilbert变换，得到相应的Hilbert谱，即将每个IMF表示在联合的时频域中；最后，汇总所有IMF的Hilbert谱就会得到原始信号的Hilbert谱。

维基百科的介绍更详细：https://zh.wikipedia.org/wiki/%E5%B8%8C%E7%88%BE%E4%BC%AF%E7%89%B9-%E9%BB%83%E8%BD%89%E6%8F%9B




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Title:		A review on Hilbert-Huang transform: Method and its applications to geophysical studies
Authors:		Huang, Norden E.; Wu, Zhaohua
Affiliation:		AA(Research Center for Adaptive Data Analysis, National Central University, Chungli, Taiwan), AB(Center for Ocean-Land-Atmosphere Studies, Calverton, Maryland, USA)
Publication:		Reviews of Geophysics, Volume 46, Issue 2, CiteID RG2006 (RvGeo Homepage)
Publication Date:		06/2008
Origin:		AGU; WILEY
Keywords:		Computational Geophysics: Data analysis: algorithms and implementation, Global Change: Climate variability (1635, 3305, 3309, 4215, 4513), Oceanography: Physical: Surface waves and tides (1222), Seismology: Earthquake ground motions and engineering seismology, Geodesy and Gravity: Earth rotation variations, Hilbert-Huang transform, empirical mode decomposition, Hilbert spectrum analysis, ensemble empirical mode decomposition
Abstract Copyright:		Copyright 2008 by the American Geophysical Union.
DOI:		10.1029/2007RG000228
Bibliographic Code:		2008RvGeo..46.2006H

Abstract

Data analysis has been one of the core activities in scientific research, but limited by the availability of analysis methods in the past, data analysis was often relegated to data processing. To accommodate the variety of data generated by nonlinear and nonstationary processes in nature, the analysis method would have to be adaptive. Hilbert-Huang transform, consisting of empirical mode decomposition and Hilbert spectral analysis, is a newly developed adaptive data analysis method, which has been used extensively in geophysical research. In this review, we will briefly introduce the method, list some recent developments, demonstrate the usefulness of the method, summarize some applications in various geophysical research areas, and finally, discuss the outstanding open problems. We hope this review will serve as an introduction of the method for those new to the concepts, as well as a summary of the present frontiers of its applications for experienced research scientists.

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有个博客讲怎么使用的：
http://blog.sina.com.cn/s/blog_84024a4a01019pfw.html

有一本书：

Hilbert-Huang Transform and Its Applications

Norden Eh Huang, Samuel S. Shen

World Scientific, 2005 - 311页

2 评价

The HilbertOCoHuang Transform (HHT) represents a desperate attempt to break the suffocating hold on the field of data analysis by the twin assumptions of linearity and stationarity. Unlike spectrograms, wavelet analysis, or the WignerOCoVille Distribution, HHT is truly a time-frequency analysis, but it does not require an a priori functional basis and, therefore, the convolution computation of frequency. The method provides a magnifying glass to examine the data, and also offers a different view of data from nonlinear processes, with the results no longer shackled by spurious harmonics OCo the artifacts of imposing a linearity property on a nonlinear system or of limiting by the uncertainty principle, and a consequence of Fourier transform pairs in data analysis. This is the first HHT book containing papers covering a wide variety of interests. The chapters are divided into mathematical aspects and applications, with the applications further grouped into geophysics, structural safety and visualization.

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