Figure 12. The bispectrum is calculated in a two- dimensional space of frequency1versus frequency2as represented by the coarsely cross-hatched area. Because of the symmetric redundancy noted in the text and the limit imposed by the sampling rate, the bispectrum need only be calculated for the limited subset of frequency combinations illustrated by the darkly shaded triangular wedge. A strong phase relationship between f1, f2, and f1+2creates a large bispectral value B(f1, f2) represented as a vertical spike rising out of the frequency versus frequency plane. In panel A, three waves having no phase relationship are mixed together producing the waveform shown in the upper right. The bispectrum of this signal is everywhere equal to zero. In panel B, two independent waves at 3 and 10 Hz are combined in a non-linear fashion, creating a new waveform that contains the sum of the originals plus a wave at 13 Hz, which is phase-locked to the 3- and 10-Hz components. In this case, computation of the bispectrum reveals a point of high bispectral energy at f (1)= 3 and f2= 10 Hz.
