# autocorrelation function

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## autocorrelation function

(aw-toh-kor-ĕ-lay -shŏn) A mathematical function that for a real function f(t) is given by
(u )f(u t )du

It describes, for example, the time or distance over which a signal is coherent. The cross-correlation function describes how two different signals compare as they are displaced relative to one another; for two real functions f(t) and g(t ), it is given by

(u )g(u t )du

Collins Dictionary of Astronomy © Market House Books Ltd, 2006

## autocorrelation function

[¦ȯd·ō‚kär·ə′lā·shən ‚fuŋk·shən]
(mathematics)
For a specified function f (t), the average value of the product f (t) f (t- τ), where τ is a time-delay parameter; more precisely, the limit as T approaches infinity of 1/(2 T) times the integral from -T to T of F (t) f (t- τ) dt.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
From the rough idea sketched in (1.7), it can be expected that we need some kind of smoothness assumptions on [PHI] (e.g., [PHI] has to be differentiable or at least Lipschitz continuous in order to allow the last step in (1.7))-this will turn out to appear in the form of a smoothness condition on the autocorrelation function in the vicinity of its maximum.
Figure 2 shows the intensity autocorrelation function and the [d.sup.app.sub.h] distribution obtained for the particles after redispersion in water.
Figure 3 shows the generation process of an unambiguous autocorrelation function for the BOC sequence.
Cyclostationarity properties are investigated in terms of cyclic autocorrelation function (CAF) and spectral correlation density (SCD) function.
The autocorrelation function of a time series (ACF) is described as Eq.5 (Shumway and Stoffer, 2006).
--column 8 includes a name of the file with a stored autocorrelation function of standard binary sequence for a given transmission system (this function is used during the test of hypothesis with zero correlation coefficient between the bit autocorrelation function of the binary sequence analysed and standard bit autocorrelation function of binary sequence for the system with the name entered in column 1),
The autocorrelation function curves of the maintained component are shown in Figure 8.
The autocorrelation function of a maximum length C/A code consists of an infinite sequence of triangular function, as shown in Figures 1 and 2 for both L1 and L5, respectively.
The chaotic behavior found in Figure 10 is confirmed in Figure 12 which presents the autocorrelation function of the outputs x(t), y(t), z(t), and w(t) of the corresponding phase portraits of fractional-order system (8) depicted in Figure 10.
(b) Autocorrelation Function (ACF) that captures common dependencies between frame sizes in VBR video.
where F{.} is the Fourier Transform; a is the cyclic frequency and Cax (t) is the Cyclic Autocorrelation Function (CAF) of x, defined in Eq.

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