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Autocorrelation, sometimes known as serial correlation in the discrete time case, is the correlation of a signal with a delayed copy of itself as a function of delay.
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.
Calibration Factor-- the factor to convert real-time to pulse delay time when viewing the output of the autocorrelator.One example of this would be 30 ps/ms in the Coherent Model FR-103 scanning autocorrelator, which suggests that a 30 ps pulse autocorrelation width would produce a 1 ms FWHM trace when viewed on an oscilloscope.
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]
In combinatorics, a branch of mathematics, the autocorrelation of a word is the set of periods of this word. More precisely, it is a sequence of values which indicate how much the end of a word looks likes the beginning of a word.
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance. Specifically, it calculates the first two moments of the power spectrum, namely the mean and variance. It is also known as the pulse-pair algorithm in radar theory.
Barker codes of length N equal to 11 and 13 are used in direct-sequence spread spectrum and pulse compression radar systems because of their low autocorrelation properties (the sidelobe level of amplitude of the Barker codes is 1/N that of the peak signal). [15]
In other words, the global analysis assumes homogeneity. If that assumption does not hold, then having only one statistic does not make sense as the statistic should differ over space. Moreover, even if there is no global autocorrelation or no clustering, we can still find clusters at a local level using local spatial autocorrelation analysis.