The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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Cites background or methods from "The empirical mode decomposition an..."
...It is philosophically similar to the “low-frequency approach” described in the preceding paragraph....
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...Other approaches exist which do not impose such a strict model on the trend....
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...(5) If h is not an IMF, in the sense that it does not satisfy the two requirements described in the beginning of this section, then increment i and go to step (1) with ρi−1 = h. (Huang et al. (1998) call this the sifting process ; it is this process which depends on the stopping criterion.)...
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...Recall (Huang et al., 1998) that the EMD is an algorithm which decomposes a time series into a finite additive superposition of “intrinsic mode functions,” or IMFs....
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...An obvious initial barrier to solving the trend filtering problem is that the terms “decomposition,” “trend,” and “fluctuation” are context-dependent....
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97 citations
97 citations
97 citations
97 citations
References
16,554 citations
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...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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...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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"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
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...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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