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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 •
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.
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...

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Citations
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Journal Article•DOI•
A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition.

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Catherine M. Sweeney-Reed1, Slawomir J. Nasuto1•
University of Reading1
02 Feb 2007-Journal of Computational Neuroscience
TL;DR: The features of EMD are explored, including making a quantitative assessment of its ability to preserve phase content of signals, and it is shown to offer improved time-frequency localisation of synchrony and to ensure signal decomposition using EMD.
Abstract: Transient neural assemblies mediated by synchrony in particular frequency ranges are thought to underlie cognition. We propose a new approach to their detection, using empirical mode decomposition (EMD), a data-driven approach removing the need for arbitrary bandpass filter cut-offs. Phase locking is sought between modes. We explore the features of EMD, including making a quantitative assessment of its ability to preserve phase content of signals, and proceed to develop a statistical framework with which to assess synchrony episodes. Furthermore, we propose a new approach to ensure signal decomposition using EMD. We adapt the Hilbert spectrum to a time-frequency representation of phase locking and are able to locate synchrony successfully in time and frequency between synthetic signals reminiscent of EEG. We compare our approach, which we call EMD phase locking analysis (EMDPL) with existing methods and show it to offer improved time-frequency localisation of synchrony.

166 citations

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

  • ...By moving away from the strict narrow band criterion for instantaneous features to make sense, EMD allows analysis of nonstationary data, avoiding the introduction of spurious harmonics wherever nonstationarity or nonlinearity is present (Huang et al., 1998)....

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  • ...(This is due to the suggestion by Huang et al. (1998) that oversampling of the data, at five times the highest frequency contained in the data, increases the accuracy of the decomposition because of the spline interpolation used to identify modes.)...

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  • ...It is suggested that the spline interpolation could be improved, as there is a problem due to the end-effects (Huang et al., 1998), though we find here that propagation of end-effects is minimal and could be alleviated by extending the time series at each end....

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  • ...Nonlinearities can also lead to spectral leakage using wavelets, as shown by Huang et al. (1998) in analysis of earthquake data....

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  • ...Furthermore, filtering may give rise to negative frequencies, which can have no physical meaning; as phase progresses in a physical system, so frequency, its derivative, must be non-negative (Huang et al., 1998)....

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Journal Article•DOI•
A comparative analysis of multitemporal MODIS EVI and NDVI data for large-scale rice yield estimation

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Nguyen Thanh Son1, Chi-Farn Chen1, Cheng Ru Chen1, Vo Quang Minh2, Nguyen Hieu Trung2 •
National Central University1, Can Tho University2
15 Oct 2014-Agricultural and Forest Meteorology
TL;DR: In this article, a comparative analysis of multitemporal Moderate Resolution Imaging Spectroradiometer (MODIS) enhanced vegetation index (EVI) and normalized difference index (NDVI) data for estimating rice crop yields in the Mekong River Delta (MRD), Vietnam was performed.

166 citations

Journal Article•DOI•
Analysis of the Intrinsic Mode Functions

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Robert Sharpley1, Vesselin Vatchev1•
University of South Carolina1
01 Jan 2004-Constructive Approximation
TL;DR: In this paper, the authors provide an alternate characterization of the Intrinsic Mode components into which the signal is decomposed and better understand the resulting polar representations, specifically the ones which are produced by the Hilbert transform of these intrinsic modes.
Abstract: The Empirical Mode Decomposition is a process for signals which produces Intrinsic Mode Functions from which instantaneous frequencies may be extracted by simple application of the Hilbert transform. The beauty of this method to generate redundant representations is in its simplicity and its effectiveness. Our study has two objectives: first, to provide an alternate characterization of the Intrinsic Mode components into which the signal is decomposed and, second, to better understand the resulting polar representations, specifically the ones which are produced by the Hilbert transform of these intrinsic modes.

166 citations

Journal Article•DOI•
A Hybrid CNN-LSTM Model for Forecasting Particulate Matter (PM2.5)

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Taoying Li1, Miao Hua1, Xu Wu1•
Dalian Maritime University1
03 Feb 2020-IEEE Access
TL;DR: A hybrid CNN-LSTM model is developed by combining the convolutional neural network (CNN) with the long short-term memory (L STM) neural network for forecasting the next 24h PM2.5 concentration in Beijing, which performs the best results due to low error and short training time.
Abstract: PM2.5 is one of the most important pollutants related to air quality, and the increase of its concentration will aggravate the threat to people’s health. Therefore, the prediction of surface PM2.5 concentration is of great significance to human health protection. In this study, A hybrid CNN-LSTM model is developed by combining the convolutional neural network (CNN) with the long short-term memory (LSTM) neural network for forecasting the next 24h PM2.5 concentration in Beijing, which makes full use of their advantages that CNN can effectively extract the features related to air quality and the LSTM can reflect the long term historical process of input time series data. The air quality data of the last 7days and the PM2.5 concentration of the next day are first set as the input and output of the model due to the periodicity, respectively. Subsequently four models namely univariate LSTM model, multivariate LSTM model, univariate CNN-LSTM model and multivariate CNN-LSTM model, are established for PM2.5 concentration prediction. Finally, mean absolute error (MAE) and root mean square error (RMSE) are employed to evaluate the performance of these models and results show that the proposed multivariate CNN-LSTM model performs the best results due to low error and short training time.

165 citations

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

  • ...This air quality data is closely related to time, which means it belongs to time series data [8], and has obvious periodicity....

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Journal Article•DOI•
Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition

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Ümit Çavuş Büyükşahin1, Seyda Ertekin2, Seyda Ertekin1•
Middle East Technical University1, Massachusetts Institute of Technology2
07 Oct 2019-Neurocomputing
TL;DR: In this article, the authors proposed a new Autoregressive integrated moving average (ARIMA)-Artificial Neural Network (ANN) hybrid method that work in a more general framework.

165 citations

References
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Journal Article•DOI•
Deterministic nonperiodic flow

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Edward N. Lorenz1•
Massachusetts Institute of Technology1
01 Mar 1963-Journal of the Atmospheric Sciences
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into consider­ably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.

16,554 citations

"The empirical mode decomposition an..." refers background in this paper

  • ...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....

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Book•
Linear and Nonlinear Waves

[...]

G. B. Whitham
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.

8,808 citations

Book•
RANDOM DATA Analysis and Measurement Procedures

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Julius S. Bendat, Allan G. Piersol
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.

6,693 citations

"The empirical mode decomposition an..." refers background in this paper

  • ...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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Theory of communication

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Dennis Gabor
01 Jan 1946

5,910 citations

"The empirical mode decomposition an..." refers methods in this paper

  • ...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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Journal Article•DOI•
Mathematical analysis of random noise

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S. O. Rice
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.
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

5,806 citations

"The empirical mode decomposition an..." refers background in this paper

  • ...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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Related Papers (5)
Ensemble empirical mode decomposition: a noise-assisted data analysis method

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01 Jan 2009-Advances in Adaptive Data Analysis
Zhaohua Wu, Norden E. Huang
Empirical mode decomposition as a filter bank

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30 Jan 2004-IEEE Signal Processing Letters
Patrick Flandrin, Gabriel Rilling, Paulo Gonçalves
A new view of nonlinear water waves: the Hilbert spectrum

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01 Jan 1999-Annual Review of Fluid Mechanics
Norden E. Huang, Zheng Shen, Steven R. Long
A study of the characteristics of white noise using the empirical mode decomposition method

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08 Jun 2004-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
Zhaohua Wu, Norden E. Huang
On empirical mode decomposition and its algorithms

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01 Jun 2003
Gabriel Rilling, Patrick Flandrin, Paulo Gonçalves