The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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...EMD [3] adaptively decomposes a multicomponent signal [4] into a number of the so-called IMFs ,...
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...The sifting process used in this paper is the standard one [3]....
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...T HE empirical mode decomposition (EMD) method [3] is an algorithm for the analysis of multicomponent signals [4] that breaks them down into a number of amplitude and frequency modulated (AM/FM) zero-mean signals, termed intrinsic mode functions (IMFs)....
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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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...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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...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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