ON HILBERT SPECTRAL REPRESENTATION: A TRUE TIME-FREQUENCY REPRESENTATION FOR NONLINEAR AND NONSTATIONARY DATA

doi:10.1142/S1793536911000659

	ON HILBERT SPECTRAL REPRESENTATION: A TRUE TIME-FREQUENCY REPRESENTATION FOR NONLINEAR AND NONSTATIONARY DATA
	Huang, Norden E.1; Chen, Xianyao 2; Lo, Men-Tzung 1; Wu, Zhaohua 3,4
刊名	ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS
	2011-04
卷号	3 期号:1-2 页码:63-93
关键词	Hilbert spectrum marginal Hilbert spectrum Fourier spectrum instantaneous frequency spectral resolution sampling rate Nyquist frequency uncertainty principle
ISSN号	2424-922X
DOI	10.1142/S1793536911000659
英文摘要	As the original definition on Hilbert spectrum was given in terms of total energy and amplitude, there is a mismatch between the Hilbert spectrum and the traditional Fourier spectrum, which is defined in terms of energy density. Rigorous definitions of Hilbert energy and amplitude spectra are given in terms of energy and amplitude density in the time-frequency space. Unlike Fourier spectral analysis, where the resolution is fixed once the data length and sampling rate is given, the time-frequency resolution could be arbitrarily assigned in Hilbert spectral analysis (HSA). Furthermore, HSA could also provide zooming ability for detailed examination of the data in a specific frequency range with all the resolution power. These complications have made the conversion between Hilbert and Fourier spectral results difficult and the conversion formula is elusive until now. We have derived a simple relationship between them in this paper. The conversion factor turns out to be simply the sampling rate for the full resolution cases. In case of zooming, there is another additional multiplicative factor. The conversion factors have been tested in various cases including white noise, delta function, and signals from natural phenomena. With the introduction of this conversion, we can compare HSA and Fourier spectral analysis results quantitatively.
资助项目	NSF of USA grant[ATM-0917743]
WOS研究方向	Mathematics
语种	英语
出版者	WORLD SCIENTIFIC PUBL CO PTE LTD
WOS记录号	WOS:000216764200005
内容类型	期刊论文
源URL	[http://ir.fio.com.cn:8080/handle/2SI8HI0U/24691]
专题	自然资源部第一海洋研究所
通讯作者	Huang, Norden E.
作者单位	1.Natl Cent Univ, Res Ctr Adapt Data Anal, Zhongli 32001, Taiwan 2.State Ocean Adm, Inst Oceanog 1, Qingdao, Peoples R China 3.Florida State Univ, Dept Earth Ocean & Atmospher Sci, Tallahassee, FL 32306 USA 4.Florida State Univ, Ctr Ocean Atmospher Predict Studies, Tallahassee, FL 32306 USA
推荐引用方式 GB/T 7714	Huang, Norden E.,Chen, Xianyao,Lo, Men-Tzung,et al. ON HILBERT SPECTRAL REPRESENTATION: A TRUE TIME-FREQUENCY REPRESENTATION FOR NONLINEAR AND NONSTATIONARY DATA[J]. ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS,2011,3(1-2):63-93.
APA	Huang, Norden E.,Chen, Xianyao,Lo, Men-Tzung,&Wu, Zhaohua.(2011).ON HILBERT SPECTRAL REPRESENTATION: A TRUE TIME-FREQUENCY REPRESENTATION FOR NONLINEAR AND NONSTATIONARY DATA.ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS,3(1-2),63-93.
MLA	Huang, Norden E.,et al."ON HILBERT SPECTRAL REPRESENTATION: A TRUE TIME-FREQUENCY REPRESENTATION FOR NONLINEAR AND NONSTATIONARY DATA".ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS 3.1-2(2011):63-93.