Polyspectra of analytic signals

For complex signals, n-th order moment functions can be defined in 2ⁿ different ways, depending on the placement of complex conjugates. We demonstrate that, for stationary analytic signals, only a few of these different moments are actually required for a complete n-th order description. Which, and how many of them, depends on the signal´s spectrum. We investigate properties of n-th order moments and spectra with different conjugation patterns and show how they provide different information about the signal.