Bispectrum
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In mathematics, in the area of statistical analysis, the bispectrum is a statistic used to search for nonlinear interactions. The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum. The Fourier transform of C3(t1, t2) (third-order cumulant-generating function) is called the bispectrum or bispectral density. Applying the convolution theorem allows fast calculation of the bispectrum B(f1,f2) = X * (f1 + f2).X(f1).X(f2).
They fall in the category of higher-order spectra, or polyspectra and provide supplementary information to the power spectrum. The third order polyspectrum (bispectrum) is the easiest to compute, and hence the most popular.
A statistic defined analogously is the bispectral coherency or bicoherence.
Bispectrum and bicoherence may be applied to the case of non-linear interactions of a continuous spectrum of propagating waves in one dimension [1].
Bispectral measurements have been carried out for EEG signals monitoring [2].
In seismology, signals rarely have adequate duration for making sensible bispectral estimates from time averages.
[edit] See also
[edit] References
- Mendel JM. "Tutorial on higher-order statistics (spectra) in signal processing and system theory: theoretical results and some applications". Proc. IEEE, 79, 3, 278-305
