The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
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...Empirical mode decomposition [ 15 ] is basically a sifting process in which different modes of oscillation are sieved out of original signal....
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...(EMD) is a time frequency analysis method developed by Huang et al., [ 15 ] which is based on the local characteristic time scale of signal and decomposes the complicated signals into number of IMFs....
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...For the purpose of reducing maintenance costs and extracting representative features from the complex nonstationary noisy signal, numerous signal processing approaches have been developed for fault diagnosis of electric generators used in wind turbines, such as statistical analysis, Fourier transform [15], wavelet transform [16], [17], Hilbert–Huang transform [18], and empirical mode decomposition [19], [20]....
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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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