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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 ...
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 .
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.
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.
The second-order logic without these restrictions is sometimes called full second-order logic to distinguish it from the monadic version. Monadic second-order logic is particularly used in the context of Courcelle's theorem, an algorithmic meta-theorem in graph theory. The MSO theory of the complete infinite binary tree is decidable.
For higher-order autoregressive processes, the sample autocorrelation needs to be supplemented with a partial autocorrelation plot. The partial autocorrelation of an AR( p ) process becomes zero at lag p + 1 and greater, so we examine the sample partial autocorrelation function to see if there is evidence of a departure from zero.
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