# The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis

TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.

Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...

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##### Citations

5,108 citations

2,185 citations

### Cites background or methods from "The empirical mode decomposition an..."

...Despite the limited mathematical understanding and some obvious shortcomings, the EMDmethod has had significant impact and is widely used in a broad variety of time-frequency analysis applications....

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...Index Terms—AM-FM, augmented Lagrangian, Fourier transform, Hilbert transform, mode decomposition, spectral decomposition, variational problem, Wiener filter....

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2,100 citations

1,783 citations

### Cites background or methods from "The empirical mode decomposition an..."

...As discussed in Huang et al (1998a), such a definition gives only a global averaged meaning to the energy and time scales....

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...(7) The procedure is illustrated in Huang et al (1998a)....

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...We will introduce the whole process by starting from the Hilbert transform....

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...31 :4 by C A L IF O R N IA I N ST IT U T E P1: KKK/NBL/spd/mbg P2: NBL/ARY QC: NBL/kba T1: NBL November 24, 1998 12:47 Annual Reviews AR075-12...

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...A degree of statistical stationarity is also defined by Huang et al (1998a)....

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1,551 citations

##### References

15,109 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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8,801 citations

6,669 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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5,901 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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5,541 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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