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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 >.
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) 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 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.
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 ...
A plot showing 100 random numbers with a "hidden" sine function, and an autocorrelation (correlogram) of the series on the bottom. In the analysis of data, a correlogram is a chart of correlation statistics.
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis (DFA) is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes (diverging correlation time, e.g. power-law decaying autocorrelation function) or 1/f noise.
Visual comparison of convolution, cross-correlation and autocorrelation. A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. [1]