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The (potentially time-dependent) autocorrelation matrix (also called second moment) of a (potentially time-dependent) random vector = (, …,) is an matrix containing as elements the autocorrelations of all pairs of elements of the random vector .
Suppose be a weakly stationary (2nd-order stationary) process with mean , variance , and autocorrelation function ().Assume that the autocorrelation function () has the form () as , where < < and () is a slowly varying function at infinity, that is () = for all >.
The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum. The Fourier transform of C 3 (t 1,t 2) (third-order cumulant) is called bispectrum or bispectral density. They fall in the category of Higher Order Spectra, or Polyspectra and provide supplementary information to the power ...
Higher order coherence or n-th order coherence (for any positive integer n>1) extends the concept of coherence to quantum optics and coincidence experiments. [1] It is used to differentiate between optics experiments that require a quantum mechanical description from those for which classical fields suffice.
An important special case of cyclostationary signals is one that exhibits cyclostationarity in second-order statistics (e.g., the autocorrelation function). These are called wide-sense cyclostationary signals, and are analogous to wide-sense stationary processes. The exact definition differs depending on whether the signal is treated as a ...
The Fourier transform of the second-order cumulant, i.e., the autocorrelation function, is the traditional power spectrum. The Fourier transform of C 3 (t 1, t 2) (third-order cumulant-generating function) is called the bispectrum or bispectral density.