Fourth-order spectra of mixture processes

The hypothesis for non-Gaussian processes higher-order spectra contain information that usually is not contained in second-order spectra is proved for a special case of the trispectrum using mixture processes. Specifically, the fourth-order cumulant spectrum is shown to differentiate between a Gaussian process and a non-Gaussian mixture process. Mixture processes often represent physical phenomena arising in sonar and radar applications. For example, the reflected components of an active transmission can be composed of a mixture of two sinusoids due to target resonances. It is demonstrated that the fourth-order cumulant spectrum can differentiate between a sum of sinusoids and a mixture of sinusoids