On holo-hilbert spectral analysis: A full informational spectral representation for nonlinear and non-stationary data

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Title:	On holo-hilbert spectral analysis: A full informational spectral representation for nonlinear and non-stationary data
Authors:	黃鍔;Huang, Norden E.;Hu, Kun;Yang, Albert C. C.;Chang, Hsing-Chih;Jia, Deng;Liang, Wei-Kuang;Yeh, Jia Rong;Kao, Chu-Lan;Juan, Chi-Huang;Peng, Chung Kang;Meijer, Johanna H.;Wang, Yung-Hung;Long, Steven R.;Wu, Zhauhua
Contributors:	認知智慧與精準健康照護研究中心
Keywords:	Empirical Mode Decomposition;Hilbert–huang Transform;Holo-Hilbert Spectral Analysis;Holo-Hilbert Spectrum;Instrumentation And Photography;Non-Stationary;Nonlinear;Numerical Analysis
Date:	2016-04-13
Issue Date:	2026-04-23 14:26:41 (UTC+8)
Publisher:	The Royal Society;Goddard Space Flight Center: The Royal Society
Abstract:	摘要： The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities. 其他題名： Phil. Trans. R. Soc. A 其他題名： Philos Trans A Math Phys Eng Sci 出版者： Goddard Space Flight Center: The Royal Society 出版日期： 2016-04-13 出處： Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2016-04, Vol.374 (2065), p.20150206-20150206 資源來源： NASA Technical Reports Server 版權： 2016 The Authors. 版權： 2016 The Author(s). 版權： 2016 The Authors. 2016 識別號： ISSN: 1364-503X 識別號： ISSN: 1471-2962 識別號： EISSN: 1471-2962 識別號： DOI: 10.1098/rsta.2015.0206 識別號： PMID: 26953180
Appears in Collections:	[Cognitive Intelligence & Precision Healthcar] journal & Dissertation

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