The parametric characteristic of bispectrum for nonlinear systems subjected to Gaussian input

The bispectrum defined in terms of the third-order cumulant or moment is fairly sensitive to the non-Gaussianity of signals and, therefore, can effectively extract information due to deviations from Gaussianity. This property enables the bispectrum to detect and characterize the nonlinearity of a system as the output response of a nonlinear system subjected to a Gaussian input will no longer be Gaussian. In this study, for the polynomial nonlinear systems which can be modeled as a convergent Volterra series, an analytical expression about the calculation of the bispectrum for nonlinear systems subjected to zero mean Gaussian excitation was derived. Moreover, based on the expression, an explicit relationship was established as a polynomial function between the nonlinear characteristic parameters and the bispectrum, which greatly facilitates the analysis of how the former affects the latter. Numerical examples were included to verify the results.

► Bispectra of nonlinear systems are investigated using Volterra series.
► An expression is derived to calculate bispectra for systems subject to white Gaussian excitation.
► A relationship is established as polynomial function between nonlinear parameters and bispectrum.
► Numerical simulation studies are used to validate the results.