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For example, to calculate the autocorrelation of the real signal sequence = (,,) (i.e. =, =, =, and = for all other values of i) by hand, we first recognize that the definition just given is the same as the "usual" multiplication, but with right shifts, where each vertical addition gives the autocorrelation for particular lag values: +
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.
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.
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.
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. This value can be used to compute, for example, the average value of the first occurrence of this word in a random ...
Example of a two-dimensional correlation spectrum. Open circles in this simplified view represent positive peaks, while discs represent negative peaks It is not always possible to unequivocally determine the direction of intensity change, such as is for example the case for highly overlapping signals next to each other and of which the ...
For example, in time series analysis, a plot of the sample autocorrelations versus (the time lags) is an autocorrelogram. If cross-correlation is plotted, the result is called a cross-correlogram . The correlogram is a commonly used tool for checking randomness in a data set .
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.