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: While EEMD presents quite different behaviors for different situations, CEEMDAN evidences some robustness with an almost unaffected performance for the studied cases, partly support empirical recommendations reported in the literature while evidencing new distinctive features.
Abstract: In this work we explore the capabilities of two noise-assisted EMD methods: Ensemble EMD (EEMD) and the recently proposed Complete Ensemble EMD with Adaptive Noise (CEEMDAN), to recover a pure tone embedded in different kinds of noise, both stationary and nonstationary. Experiments are carried out for assessing their performances with respect to the level of the added noise and the number of realizations used for averaging. The obtained results partly support empirical recommendations reported in the literature while evidencing new distinctive features. While EEMD presents quite different behaviors for different situations, CEEMDAN evidences some robustness with an almost unaffected performance for the studied cases.
117 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical Mode Decomposition (EMD) [Huang et al. (1998)] is an adaptive method introduced to analyze signals that may be nonstationary and/or stemming from nonlinear systems....
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TL;DR: The proposed method, called MEMD-CCA, first utilizes MEMD and CCA to jointly decompose the few-channel EEG recordings into multivariate intrinsic mode functions (IMFs), and is applied to further decomposes the reorganized multivariate IMFs into the underlying sources.
Abstract: Electroencephalography (EEG) recordings are often contaminated by muscle artifacts. In the literature, a number of methods have been proposed to deal with this problem. Yet most denoising muscle artifact methods are designed for either single-channel EEG or hospital-based, high-density multichannel recordings, not the few-channel scenario seen in most ambulatory EEG instruments. In this paper, we propose utilizing interchannel dependence information seen in the few-channel situation by combining multivariate empirical mode decomposition and canonical correlation analysis (MEMD-CCA). The proposed method, called MEMD-CCA, first utilizes MEMD to jointly decompose the few-channel EEG recordings into multivariate intrinsic mode functions (IMFs). Then, CCA is applied to further decompose the reorganized multivariate IMFs into the underlying sources. Reconstructing the data using only artifact-free sources leads to artifact-attenuated EEG. We evaluated the performance of the proposed method through simulated, semisimulated, and real data. The results demonstrate that the proposed method is a promising tool for muscle artifact removal in the few-channel setting.
117 citations
Cites background from "The empirical mode decomposition an..."
...[44], is a fully data-driven decomposition technique for nonlinear and nonstationary signals....
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TL;DR: The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation and its potential to seismic signal processing applications is shown.
Abstract: Time-frequency analysis can provide useful information in seismic data processing and interpretation. An accurate time-frequency representation is important in highlighting subtle geologic structures and in detecting anomalies associated with hydrocarbon reservoirs. The popular methods, like short-time Fourier transform and wavelet analysis, have limitations in dealing with fast varying instantaneous frequencies, which is often the characteristic of seismic data. The synchrosqueezing transform (SST) is a promising tool to provide a detailed time-frequency representation. We apply the SST to seismic data and show its potential to seismic signal processing applications.
117 citations
TL;DR: A novel specific emitter identification method based on transient communication signal's time-frequency-energy distribution obtained by Hilbert-Huang transform (HHT) is proposed and can represent more subtle characteristics than the RF fingerprints based on instantaneous amplitude, phase, frequency and energy envelope.
Abstract: A novel specific emitter identification method based on transient communication signal's time-frequency-energy distribution obtained by Hilbert-Huang transform (HHT) is proposed. The transient starting point is detected using the phase-based method and the transient endpoint is detected using a self-adaptive threshold based on the HHT-based energy trajectory. Thirteen features that represent both overall and subtle transient characteristics are proposed to form a radio frequency (RF) fingerprint. The principal component analysis method is used to reduce the dimension of the feature vector and a support vector machine is used for classification. A signal acquisition system is designed to capture the signals from eight mobile phones to test the performance of the proposed method. Experimental results demonstrate that the method is effective and the proposed RF fingerprint can represent more subtle characteristics than the RF fingerprints based on instantaneous amplitude, phase, frequency and energy envelope. This method can be equally applicable for any wireless emitter to enhance the security of the wireless networks.
116 citations
TL;DR: It is shown, in this paper, that the IMFs have several desirable properties unique to SCSS problem and how these properties can be advantaged to relax the constraints posed by the problem.
Abstract: A novel approach to solve the single-channel source separation (SCSS) problem is presented. Most existing supervised SCSS methods resort exclusively to the independence waveform criteria as exemplified by training the prior information before the separation process. This poses a significant limiting factor to the applicability of these methods to real problem. Our proposed method does not require training knowledge for separating the mixture and it is based on decomposing the mixture into a series of oscillatory components termed as the intrinsic mode functions (IMFs). We show, in this paper, that the IMFs have several desirable properties unique to SCSS problem and how these properties can be advantaged to relax the constraints posed by the problem. In addition, we have derived a novel sparse non-negative matrix factorization to estimate the spectral bases and temporal codes of the sources. The proposed algorithm is a more complete and efficient approach to matrix factorization where a generalized criterion for variable sparseness is imposed onto the solution. Experimental testing has been conducted to show that the proposed method gives superior performance over other existing approaches.
116 citations
Cites background from "The empirical mode decomposition an..."
...Thus, the extracted IMFs are real-valued signals [33] that contain the basic properties of the original source....
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...For in-depth information on EMD, interested readers are referred to [33]....
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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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