The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
329 citations
Cites methods from "The empirical mode decomposition an..."
...Instead, the sifting process was terminated when the extracted IMFs satisfied the stopping criteria prescribed in Huang et al. (1998). Removing this stopping rule and applying the EMD to the brain wave signal of figure 7c required 56 393 siftings before the very first resulting IMF was produced that...
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...An alternative approach to TFE analysis that made progress towards addressing these difficulties is known as the empirical mode decomposition (EMD; Huang et al. 1998, 2003)....
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...Instead, the sifting process was terminated when the extracted IMFs satisfied the stopping criteria prescribed in Huang et al. (1998)....
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...Finally, and perhaps most importantly, the sifting procedure introduced by Huang et al. (1998) in an attempt to produce proper rotation components with the EMD, but which also causes smearing and smoothing of TFE information, is not needed in the ITD....
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...In an effort to work around this inability to consistently generate proper rotation components, Huang et al. (1998) developed a ‘sifting’ process that is applied in an iterative manner to generate a sequence of signal baseline candidates until one is found with a proper rotation residual....
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324 citations
321 citations
Additional excerpts
...The Empirical Mode Decomposition/HilbertHuang Transform [Huang et al., 1998] is a nonparametric, nonstationary analysis, whereas a time series is decomposed into a finite number of intrinsic oscillatory modes using the local maxima or minima envelope....
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...The analysis method is based on Empirical Mode Decomposition (EMD)/Hilbert-Huang Transformation (HHT) [Huang et al., 1998; Wu and Huang, 2004; Wu et al., 2007; Huang and Wu, 2008]; to the best of our knowledge, the EMD/HHT method has not been used for analyzing sea level trend before it was…...
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320 citations
320 citations
Cites background or methods from "The empirical mode decomposition an..."
...In comparison, the Hilbert–Huang transform (HHT) is based on the instantaneous frequencies resulting from the intrinsic mode functions of the signal being analyzed [ 11 ]–[13]; thus, it is not constrained by the uncertainty limitations with respect to the time and frequency resolutions to which other time-frequency techniques are subject....
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...Equation (13) provides a complete description of the empirical mode decomposition process [ 11 ], which can be evaluated by checking the amplitude error between the reconstructed and the original signal....
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...[ 11 ]. Therefore, the cubic spline function was employed in the presented study....
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...The HHT represents the signal being analyzed in the time-frequency domain by combining the empirical mode decomposition (EMD) with the Hilbert transform [ 11 ]....
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...To effectively construct frequency spectrum of a vibration signal that contains multiple-frequency components, the signal needs to be first decomposed into mono-component functions, by means of EMD [ 11 ]....
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References
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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8,808 citations
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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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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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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