does anyone know how the "bispectrum" works?

Started by fisico32 May 7, 2010
Hello Forum,

the bispectrum is a generalization of the spectrum.The PSD of a process is
the Fourier transform of the autocorrelation function 
R(tau)=<x(t) x(t+tau)>, for a stationary process. The "triple"
autocorrelation function is  R(tau1, tau2)=<x(t) x(t+tau1) x(t+tau2)>. It
measure the relation between three points in time.

The Fourier transform of R(tau1, tau2) is called the bispectrum which is
said to be nonzero for nonlinear and nonGaussian signals.
The bispectrum is nonzero at frequency pairs (w1, w2) that satisfy certain

Does anyone know about those conditions? I have seen different versions of
those conditions like w1+w2+w3=0 or w3=w1+w2, w3=w1-w2, and corresponding
phase conditions theta_1+theta_2+theta3=0 and am a little confused....
Does anyone know how and where those conditions come from?