The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

doi:10.1098/RSPA.1998.0193

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The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Journal Article•DOI•

The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

Norden E. Huang¹, Zheng Shen², Steven R. Long³, Man-Li C. Wu¹, Hsing H. Shih⁴, Quanan Zheng⁵, Nai-Chyuan Yen⁶, C. C. Tung⁷, Henry H. Liu⁸ - Show less +5 more•Institutions (8)

Goddard Space Flight Center¹, Johns Hopkins University², Wallops Flight Facility³, National Ocean Service⁴, University of Delaware⁵, United States Naval Research Laboratory⁶, North Carolina State University⁷, Naval Surface Warfare Center⁸

08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995

TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.

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Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

...read moreread less

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Journal Article•DOI•

Comparative study of ECG signal denoising by wavelet thresholding in empirical and variational mode decomposition domains

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Salim Lahmiri¹•Institutions (1)

Université du Québec à Montréal¹

16 Sep 2014-Healthcare technology letters

TL;DR: Simulation results show that the VMD- DWT approach outperforms the conventional EMD-DWT approach, and a non-local means approach used as a reference technique provides better results than the V MD-D WT approach.

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Abstract: Hybrid denoising models based on combining empirical mode decomposition (EMD) and discrete wavelet transform (DWT) were found to be effective in removing additive Gaussian noise from electrocardiogram (ECG) signals. Recently, variational mode decomposition (VMD) has been proposed as a multiresolution technique that overcomes some of the limits of the EMD. Two ECG denoising approaches are compared. The first is based on denoising in the EMD domain by DWT thresholding, whereas the second is based on noise reduction in the VMD domain by DWT thresholding. Using signal-to-noise ratio and mean of squared errors as performance measures, simulation results show that the VMD-DWT approach outperforms the conventional EMD-DWT. In addition, a non-local means approach used as a reference technique provides better results than the VMD-DWT approach.

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124 citations

Cites methods from "The empirical mode decomposition an..."

...Besides, the EMD [16] is an adaptive and data-driven technique used for processing non-linear and non-stationary signals in addition to stationary signals....
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...Methods: The EMD [16] decomposes a signal into a sum of functions....
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Journal Article•DOI•

The Hilbert spectrum via wavelet projections

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Sofia C. Olhede¹, Andrew T. Walden¹•Institutions (1)

Imperial College London¹

08 Apr 2004-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences

TL;DR: In this paper, the maximal-overlap (undecimated/stationary/translation invariant) discrete wavelet transform and wavelet packet transforms are used, with superior results can be obtained using wavelet-based projections.

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Abstract: Non-stationary signals are increasingly analysed in the time-frequency domain to determine the variation of frequency components with time. It was recently proposed in this journal that such signals could be analysed by projections onto the time-frequency plane giving a set of monocomponent signals. These could then be converted to ‘analytic’ signals using the Hilbert transform and their instantaneous frequency calculated, which when weighted by the energy yields the ‘Hilbert energy spectrum’ for that projection. Agglomeration over projections yields the complete Hilbert spectrum. We show that superior results can be obtained using waveletbased projections. The maximal-overlap (undecimated/stationary/translation invariant) discrete wavelet transform and wavelet packet transforms are used, with

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124 citations

Cites background or methods from "The empirical mode decomposition an..."

...The overall Hilbert energy spectrum for x(t) is defined ( Huang et al 1998 ) as the amalgamation of the spectra of each of the dj(t)’s....
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...Recently in this journal a time-frequency energy spectrum estimator was proposed by Huang et al (1998) which projects the signal in the time-frequency plane (using the ‘empirical mode decomposition (EMD)’) and then calculates the instantaneous frequency for each projection....
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... Huang et al (1998, p. 920) test whether the accumulated relative squared differences between h1,k(t) and h1,k−1(t) is less than 0.3; see also Magrin-Chagnolleau and Baraniuk (1999)....
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... Huang et al (1998, 1999) define an empirical mode decomposition (EMD) of a signal into intrinsic mode functions (IMFs)....
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...The approach of Huang et al (1998) is aimed at analysis of both non-stationary and non-linear proceses....
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Journal Article•DOI•

Artifact reduction in electrogastrogram based on empirical mode decomposition method.

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Hualou Liang¹, Zhiyue Lin², Richard W. McCallum²•Institutions (2)

Center for Complex Systems and Brain Sciences¹, University of Kansas²

01 Jan 2000-Medical & Biological Engineering & Computing

TL;DR: The results show that this method, combined with instantaneous frequency analysis, effectively separate, identify and remove contamination from a wide variety of artifactual sources in EGG recordings.

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Abstract: Severe contamination of the gastric signal in electrogastrogram (EGG) analysus by respiratory, motion, cardiac artifacts, and possible myoelectrical activity from other organs, poses a major challenge to EGG interpretation and analysis. A generally applicable method for removing a variety of artifacts from EGG recordings is proposed based on the empirical mode decomposition (EMD) method. This decomposition technique is adaptive, and appears to be uniquely suitable for nonlinear, non-stationary data analysis. The results show that this method, combined with instantaneous frequency analysis, effectively separate, identify and remove contamination from a wide variety of artifactual sources in EGG recordings.

...read moreread less

124 citations

Journal Article•DOI•

Damage detection method based on operating deflection shape curvature extracted from dynamic response of a passing vehicle

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Yao Zhang¹, Seng Tjhen Lie¹, Zhihai Xiang²•Institutions (2)

Nanyang Technological University¹, Tsinghua University²

01 Feb 2013-Mechanical Systems and Signal Processing

TL;DR: Based on the operating deflection shape curvature and the assumption that the intact structure is smooth and homogenous, a new damage detection algorithm called Global Filtering Method (GFM) is proposed in this paper.

...read moreread less

124 citations

Journal Article•DOI•

Adaptive parameterless empirical wavelet transform based time-frequency analysis method and its application to rotor rubbing fault diagnosis

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Jinde Zheng¹, Haiyang Pan¹, Shubao Yang¹, Junsheng Cheng²•Institutions (2)

Anhui University of Technology¹, Hunan University²

01 Jan 2017-Signal Processing

TL;DR: The proposed adaptive parameterless EWT (APEWT) method could effectively fulfill the fault diagnosis of rotor rubbing and show a better effect than EMD and EEMD methods, according to analysis of experiment data.

...read moreread less

124 citations

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...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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01 Jul 1944-Bell System Technical Journal

TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.

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Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22

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...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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