the three Fourier components , and were perfectly phase locked. Then if the Fourier transform was calculated several times from different parts of the time series, the bispectrum will always have the same value. If we add together all of the bispectra, they will sum without cancelling. On the other hand, suppose that the phases of each of these frequencies was random. Then, the bispectrum will have the same magnitude (assuming that the magnitude of the frequency components is the same) but the phase will be randomly oriented. Adding together all of the bispectra will result in cancellation, because of the random phase orientation, and so the sum of the bispectra will have a small magnitude. Detecting phase coupling requires summation over a number of independent samples- this is the first motivation for defining the bicoherence. Secondly, the bispectrum is not normalized, because it still depends on the magnitudes of each of the frequency components. The bicoherence includes a normalization factor that removes the magnitude dependence. There is some inconsistency with the definition of the bicoherence normalization constant. Some of the definitions that have been used are which was provided in Sigl and Chamoun 1994, but does not appear to be correctly normalized. Alternatively, plasma physics typically uses where the angle brackets denote averaging. Note that this is the same as using a sum, because is the same in the numerator and the denominator. This definition is directly from Nagashima 2006, and is also referred to in He 2009 and Maccarone 2005. Finally, one of the most intuitive definitions comes from Hagihira 2001 and Hayashi 2007, which is The numerator contains the magnitude of the bispectrum summed over all of the time series segments. This quantity is large if there is phase coupling, and approaches 0 in the limit of random phases. The denominator, which normalizes the bispectrum, is given by calculating the bispectrum after setting all of the phases to 0. This corresponds to the case where there is perfect phase coupling, because all of the samples have zero phase. Therefore, the bicoherence has a value between 0 (random phases) and 1 (total phase coupling). See also Coherence (signal processing) References Hagihira, S., Takashina, M., Mori, T., Mashimo, T., & Yoshiya, I. (2001). Practical Issues in Bispectral Analysis of Electroencephalographic Signals. Anesthesia & Analgesia, 93(4), 966-970. Retrieved from http://www.anesthesia-analgesia.org/content/93/4/966.abstract Hayashi, K., Tsuda, N., Sawa, T., & Hagihira, S. (2007).