Bispectrum

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 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 :${\displaystyle B(f_{1},f_{2})=F^{*}(f_{1}+f_{2}).F(f_{1}).F(f_{2})}$, where ${\displaystyle F}$ denotes the Fourier transform of the signal, and ${\displaystyle F^{*}}$ its conjugate.

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