Some considerations about third-order statistics for different types of random signals

The autocorrelation and power spectral density functions of a random process are two of the most commonly used concepts in signal processing and in its applications. The relations that define them involve the expected value of a double product of the process or of its Fourier transform. Hence, they are based on second-order statistics. The generalization of this idea leads to the so-called cumulant functions and cumulant spectra, therefore higher-order statistics. Theoretically, the higher-order statistics are null for Gaussian signals. Practically, these quantities are not vanishing. In this paper the third-order statistics for different types of random signals are analyzed.