Bicoherence

Article summary

In mathematics and statistical analysis, bicoherence (also known as bispectral coherency) is a squared normalised version of the bispectrum. The bicoherence takes values bounded between 0 and 1, which make it a convenient measure for quantifying the extent of phase coupling in a signal. The prefix bi- in bispectrum and bicoherence refers not to two time series x t , y t but rather to two frequencies of a single signal. 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 C 3 (t 1 ,t 2 ) (third-order cumulant) is called bispectrum or bispectral density. 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. The difference with measuring coherence (coherence analysis is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) is the need for both input and output measurements by estimating two auto-spectra and one cross spectrum. On the other hand, bicoherence is an auto-quantity, i.e. it can be computed from a single signal.…

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