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Journal ArticleDOI

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

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 ArticleDOI
TL;DR: A performance comparison study, through numerical simulations and applications to real EEG recordings contaminated with muscle artifacts, demonstrates the advantage of single-channel techniques over multichannel ones, especially for low signal-to-noise ratios.
Abstract: Electroencephalogram (EEG) recordings are often contaminated with muscle artifacts. Muscular activities strongly obscure EEG signals and complicate subsequent EEG-based data analysis. Conventional methods for removing muscle artifact from EEG are usually based on blind source separation techniques and involve jointly analyzing multichannel EEG recordings. Instead of using the multichannel approaches, this paper proposes to explore single-channel techniques for muscle artifact removal from multichannel EEG. It may seem paradoxical that we denoise each channel individually while ignoring interchannel relationships. We conduct a performance comparison study, through numerical simulations and applications to real EEG recordings contaminated with muscle artifacts. The results demonstrate the advantage of single-channel techniques over multichannel ones, especially for low signal-to-noise ratios. This paper may change the traditional understanding of denoising the EEG signals.

95 citations


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

  • ...Empirical mode decomposition (EMD) is a single-channel technique, first proposed in 1998 [35], for nonlinear and...

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  • ...An IMF is a function that satisfies two following conditions [35]: (1) The number...

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  • ...To calculate an IMF from a time series signal x, a sifting process is implemented [35]....

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Journal ArticleDOI
TL;DR: In this paper, a finite element-based framework for buffeting analysis of long-span cable-supported bridges under skew winds has been presented, which is applied to the Tsing Ma Suspension Bridge in Hong Kong.

95 citations

Journal ArticleDOI
TL;DR: Wang et al. as discussed by the authors analyzed the spatiotemporal heterogeneity of vegetation coverage and their relationship with climate change at different time scales in the Yangtze River and Yellow River Basin (YZYRB) based on the ensemble empirical mode decomposition (EEMD).

95 citations

Proceedings ArticleDOI
14 May 2006
TL;DR: The rationale underlying the nonlinear empirical mode decomposition method is intrinsically a continuous-time approach and the method can however only be applied in practice to discrete-time signals.
Abstract: The rationale underlying the nonlinear Empirical Mode Decomposition method is intrinsically a continuous-time approach. The method can however only be applied in practice to discrete-time signals. EMD is obtained through iterating a basic nonlinear operator for which we derive an upper bound for the effects of sampling. Finally the effects of sampling for a complete EMD are assessed using the knowledge on the basic operator.

95 citations


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

  • ...Empirical Mode Decomposition (EMD) has been recently pioneered by Huang et al. [1, 2] for adaptively decomposing nonstationary and/or nonlinear time series....

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Journal ArticleDOI
TL;DR: Experiments indicate that the technique proposed in this work can form better decomposition compared with past algorithms not only for textures but also for natural images.
Abstract: A novel boundary processing technique is proposed for bidimensional empirical mode decomposition (BEMD). BEMD is a new form of multiscale decomposition and has superior quality in extracting intrinsic components of textures. Although the boundary effect of BEMD is one of its main questions, there have been no concrete discussions or effective methods for it. A modified algorithm of nonparametric sampling for texture synthesis is used to extend images before applying BEMD. Experiments indicate that the technique proposed in This work can form better decomposition compared with past algorithms not only for textures but also for natural images.

94 citations


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

  • ...Since the original EMD paper [8] appeared, there have been extensive research and application of this technique to 1-D signal processing because of the superior quality of EMD for nonstationary signals....

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  • ...Huang et al. [8] have also proposed an algorithm called “sifting” to extract IMFs from the original signal as follows: where are IMFs and monotonic function is the residue....

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  • ...D EMD boundary processing mainly include three classes: 1) the method adopted by Huang [8] which Manuscript received May 12, 2004; revised July 5, 2004....

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  • ...[8] for the processing of nonstationary functions....

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  • ...[8] have also proposed an algorithm called “sifting” to extract IMFs from the original signal as...

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References
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Journal ArticleDOI
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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Journal ArticleDOI
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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