The trispectrum for Gaussian driven, multiple degree-of-freedom, non-linear structures

Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and type of system non-linearity. Two such spectra that have figured prominently in signal processing are the bispectrum and trispectrum. In a previous work, the authors developed an analytical solution for the bispectrum for multi-degree-of-freedom systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for the trispectrum of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary location. The analytical expression is compared to those obtained via estimation using the direct method.