Most signal processing techniques which rely on the cross spectral density are based on linear second order statistics.  Many resonant and nonlinear systems however have tonal components that occur at combinations of the fundamental frequencies.  The bicoherence spectrum is a third-order spectrum used to measure the phase coherence among three spectral components due to nonlinear wave coupling.  It is bounded by 0£b²(f_k, f_l)£1, and will take on a value close to unity when the wave at f_m is coupled to waves at f_k and f_l.  A value near zero indicates the spectral modes at f_k, f_l, and f_k+l are independent of one another.

Turbulence data is gathered using a hot wire anemometer located in the shear layer of an acoustically excited 2-D Planar Turbulent Jet.

The measured third-order bicoherence spectrum can be plotted in the (f₁, f₂) area in conjunction with the result of power spectrum.  For instance, the bicoherence spectrum clearly shows that the self-interaction of excited frequency, f_e, is partially responsible for the growth of harmonic at 2f_e (red arrows) while the difference interaction is responsible for the growth of the subharmonic at f_e/2 (green arrows) .