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Geary's C is a measure of spatial autocorrelation that attempts to determine if observations of the same variable are spatially autocorrelated globally (rather than at the neighborhood level). Spatial autocorrelation is more complex than autocorrelation because the correlation is multi-dimensional and bi-directional.
The autocorrelation of the sum of two completely uncorrelated functions (the cross-correlation is zero for all ) is the sum of the autocorrelations of each function separately. Since autocorrelation is a specific type of cross-correlation, it maintains all the properties of cross-correlation.
For jointly wide-sense stationary stochastic processes, the definition is = = [() (+) ¯] The normalization is important both because the interpretation of the autocorrelation as a correlation provides a scale-free measure of the strength of statistical dependence, and because the normalization has an effect on the statistical ...
Classification of the different kinds of optical autocorrelation. In optics, various autocorrelation functions can be experimentally realized. The field autocorrelation may be used to calculate the spectrum of a source of light, while the intensity autocorrelation and the interferometric autocorrelation are commonly used to estimate the duration of ultrashort pulses produced by modelocked lasers.
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]
As the peaks at (x,y) in the 2D synchronous spectrum are a measure for the correlation between the intensity changes at x and y in the original data, these main diagonal peaks are also called autopeaks and the main diagonal signal is referred to as autocorrelation signal. The off-diagonal cross-peaks can be either positive or negative. On the ...
FROG and autocorrelation share the idea of combining a pulse with itself in a nonlinear medium. Since a nonlinear medium will only produce the desired signal when both pulses are present at the same time (i.e. “optical gating”), varying the delay between the pulse copies and measuring the signal at each delay gives a vague estimate of the ...
In statistics, Moran's I is a measure of spatial autocorrelation developed by Patrick Alfred Pierce Moran. [ 1 ] [ 2 ] Spatial autocorrelation is characterized by a correlation in a signal among nearby locations in space.
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