Applications to Fourier series (2005)(en)(4s) by Garrett P.

By Garrett P.

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Example text

Obviously, for a stationary process, the Hilbert spectrum cannot be a function of time; in such a case the Hilbert spectrum only contains horizontal lines when plotted against . For a pure stationary case, the DS will then be identically zero. Only under this condition, marginal Hilbert spectrum will be identical to Fourier spectrum and then Fourier spectrum makes physical sense. 2) where the overline indicates averaging over a definite but shorter time span, T , than the overall time duration of the data, T .

For comparison, Fourier, Multitaper and marginal Hilbert spectra are computed. Histograms of the data in time or spatial domain help us to examine the distribution of the simulated signal compared to the original signal. Autocorrelation function is used to compare the persistence of simulated and the original data. The autocorrelation functions (Box and Jenkins, 1976) yn at are used to detect non-randomness in data. For given measurements, y1 y2 t=1 2 n, the lag k autocorrelation function is defined in Eq.

Autocorrelation function is used to compare the persistence of simulated and the original data. The autocorrelation functions (Box and Jenkins, 1976) yn at are used to detect non-randomness in data. For given measurements, y1 y2 t=1 2 n, the lag k autocorrelation function is defined in Eq. 8). 8) yi − y¯ 2 i=1 In this section, method one, which is simulated only with random phase, is examined by using several sets of data. For different types of data, the results from one or two samples are used for demonstration.

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