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.
Bispectrum and bicoherence may be applied to the case of non-linear interactions of a continuous spectrum of propagating waves in one dimension.
[3] In seismology, signals rarely have adequate duration for making sensible bispectral estimates from time averages.
[citation needed] Bispectral analysis describes observations made at two wavelengths.
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.
[citation needed] Bispectral analysis can also be used to analyze interactions between wave patterns and tides on Earth.
Bispectra fall in the category of higher-order spectra, or polyspectra and provide supplementary information to the power spectrum.
The Fourier transform of C4 (t1, t2, t3) (fourth-order cumulant-generating function) is called the trispectrum or trispectral density.
The trispectrum T(f1,f2,f3) falls into the category of higher-order spectra, or polyspectra, and provides supplementary information to the power spectrum.
The symmetries of the trispectrum allow a much reduced support set to be defined, contained within the following vertices, where 1 is the Nyquist frequency.
The trispectrum has been used to investigate the domains of applicability of maximum kurtosis phase estimation used in the deconvolution of seismic data to find layer structure.