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 :, where denotes the Fourier transform of the signal, and its conjugate.
Bispectra 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.
Bispectral analysis describes observations made at two wavelengths. It is often used by scientists to analyze elemental makeup of a planetary atmosphere by analyzing the amount of light reflected and received through various color filters. By combining and removing two filters, much can be gleaned from only two filters. Through modern computerized interpolation, a third virtual filter can be created to recreate true color photographs that, while not particularly useful for scientific analysis, are popular for public display in textbooks and fund raising campaigns.
Bispectral analysis can also be used to analyze interactions between wave patterns and tides on Earth.
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- HOSA - Higher Order Spectral Analysis Toolbox: A MATLAB toolbox for spectral and polyspectral analysis, and time-frequency distributions. The documentation explains polyspectra in great detail.