The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
306 citations
Cites background or methods from "The empirical mode decomposition an..."
...First, the recorded time series are processed by a band-pass filter or by other advanced methods, such as Huang–Hilbert empirical model decomposition [105,106]....
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...[106] Huang N, Shen Z, Long S, Wu M, Shih H, Zheng Q, et al....
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301 citations
Cites methods from "The empirical mode decomposition an..."
...Empirical Mode Decomposition-Based Hilbert Huang Transform Empirical mode decomposition (EMD) [42] has been used in some applications that involve non-stationary signals (see, e....
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...Empirical Mode Decomposition-Based Hilbert Huang Transform Empirical mode decomposition (EMD) [42] has been used in some applications that involve nonstationary signals (see, e....
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300 citations
Cites background or methods from "The empirical mode decomposition an..."
...In a nutshell, the starting point of EMD is to consider oscillatory signals at the level of their local oscillations and to formalize the idea that: “signal = fast oscillations superimposed to slow oscillations,” and to iterate on the slow oscillations component considered as a new signal....
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...Empirical Mode Decomposition (EMD) has been recently pioneered by Huang et al. [2] for adaptively decomposing signals in a sum of “well-behaved” AM-FM components....
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...This property of perfect reconstruction, together with the spectral interpretation outlined above, suggests to achieve partial reconstructions only, so as to selectively remove slow or fast oscillations (detrending or denoising, respectively)....
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300 citations
299 citations
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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