The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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...
Citations
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TL;DR: EMD analysis was applied to decompose the heartbeat intervals series, derived from one electrocardiographic signal of 13 subjects, into their components in order to identify the modes associated with breathing, proving the existence of phase and frequency coupling.
Abstract: Heart rate variability (HRV) is a well-known phenomenon whose characteristics are of great clinical relevance in pathophysiologic investigations. In particular, respiration is a powerful modulator of HRV contributing to the oscillations at highest frequency. Like almost all natural phenomena, HRV is the result of many nonlinearly interacting processes; therefore any linear analysis has the potential risk of underestimating, or even missing, a great amount of information content. Recently the technique of Empirical Mode Decomposition (EMD) has been proposed as a new tool for the analysis of nonlinear and nonstationary data. We applied EMD analysis to decompose the heartbeat intervals series, derived from one electrocardiographic (ECG) signal of 13 subjects, into their components in order to identify the modes associated with breathing. After each decomposition the mode showing the highest frequency and the corresponding respiratory signal were Hilbert transformed and the instantaneous phases extracted were then compared. The results obtained indicate a synchronization of order 1:1 between the two series proving the existence of phase and frequency coupling between the component associated with breathing and the respiratory signal itself in all subjects.
157 citations
Cites methods from "The empirical mode decomposition an..."
...The empirical mode decomposition is a signal processing technique proposed in 1998 by Huang [11] to extract all the oscillatory modes embedded in a signal without any requirement of stationarity or linearity of the data....
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...Recently the Empirical Mode Decomposition (EMD), a signal processing technique particularly suitable for nonlinear and nonstationary series, has been proposed [11] as a new tool for data analysis....
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TL;DR: This paper proposes using inherent fuzzy entropy (Inherent FuzzyEn) and its multiscale version, which employs empirical mode decomposition and fuzzy membership function (exponential function) to address the dynamic complexity in electroencephalogram (EEG) data.
Abstract: In recent years, the concept of entropy has been widely used to measure the dynamic complexity of signals. Since the state of complexity of human beings is significantly affected by their health state, developing accurate complexity evaluation algorithms is a crucial and urgent area of study. This paper proposes using inherent fuzzy entropy (Inherent FuzzyEn) and its multiscale version, which employs empirical mode decomposition and fuzzy membership function (exponential function) to address the dynamic complexity in electroencephalogram (EEG) data. In the literature, the reliability of entropy-based complexity evaluations has been limited by superimposed trends in signals and a lack of multiple time scales. Our proposed method represents the first attempt to use the Inherent FuzzyEn algorithm to increase the reliability of complexity evaluation in realistic EEG applications. We recorded the EEG signals of several subjects under resting condition, and the EEG complexity was evaluated using approximate entropy, sample entropy, FuzzyEn, and Inherent FuzzyEn, respectively. The results indicate that Inherent FuzzyEn is superior to other competing models regardless of the use of fuzzy or nonfuzzy structures, and has the most stable complexity and smallest root mean square deviation.
157 citations
Cites methods from "The empirical mode decomposition an..."
...Thus, in order to eliminate trend oscillations, the inherent functions (called intrinsic mode functions or IMFs) extracted from the empirical mode decomposition (EMD) are considered an effective filter for reducing superimposed trends in signals [16]....
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TL;DR: The addressed method integrates the deep framework with multiscale and hybrid observations, and therefore being good at exploring sophisticated natures in the reservoir inflow forecasting.
157 citations
TL;DR: A novel approach based on Hilbert-Huang transform (HHT), which comprises the empirical mode decomposition (EMD) and Hilbert transform, is proposed to estimate the mean frequency of non-stationary signal and shows low variability and robustness to the length of the analysis window.
156 citations
TL;DR: This study provides a deep insight into how such nonlinear features could be exploited to effectively and reliably detect the presence of CAD.
156 citations
Cites background from "The empirical mode decomposition an..."
...It does not assume linearity and stationarity conditions [Huang et al., 1998]....
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References
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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•
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•
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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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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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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