The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
88 citations
Cites methods from "The empirical mode decomposition an..."
...The analysis results behave better than HHT and SWT, as shown in Fig....
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...For the purpose of comparison, the TFR of HHT is shown in Fig....
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...In this case, the HHT spectrum can reveal some oscillation feature....
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...Some effective methods have been widely studied and used, such as empirical mode decomposition and Hilbert–Huang transform (HHT) [3]–[6], wavelet transform [7]–[11], synchrosqueezed wavelet transform (SWT) [12], [13], and time–frequency analysisbased methods [14], [15]....
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...The HHT spectrum is also incapable of characterizing the entire oscillation behavior of the vibration signal in this case....
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88 citations
88 citations
Cites background from "The empirical mode decomposition an..."
...Furthermore, our computational scheme can be realized in near real-time, and our mathematical theory has direct extension to the multivariate setting....
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88 citations
88 citations
Cites methods from "The empirical mode decomposition an..."
...The EMD has been introduced by Huang et al. (1998) for the analysis of 1D signals, in the context of time series analysis, as part of the Hilbert– Huang transform....
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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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