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

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.
References in periodicals archive ?
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The synthesis algorithm of binary synchrocodes of arbitrary length with good aperiodic autocorrelation functions.
The theoretical partial autocorrelation function [p.
It is difficult to determine the optimal lag values in the model structure where the autocorrelation function values start to become statistically insignificant.
The results were again assessed for autocorrelation by assessing the residuals from the ARIMA plotted on both the autocorrelation function (ACF) and the partial autocorrelation function (PACF) maps.
We assume that the random wave process in the open sea is stationary, whose autocorrelation function is a function of time difference [xi] only:
in the final stage of the synthesis algorithm), and about the influence of the Doppler frequency shift on the shape assigned to the normalized complex envelope of the synthesized signal autocorrelation function, are presented.
Akgiray (1989) points that Ljung-Box test could not reject the hypothesis of independence in the residual series since it is based on the behavior of the autocorrelation function.
This develops well on the use of the autocorrelation function [1], and of a two-point correlation function [38], widely used in RC analysis so far.
The method can be applied to search for sequences with zero periodic autocorrelation function.
Therefore, we have evaluated the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the OLS regression residuals using SAS procedure PROC ARIMA (see SAS/ETS User's Guide, 1993).
By using time series analysis in JMP with data entered, students will first observe the autocorrelation function (ACF) and the partial autocorrelation function (PACF) of the visitor data.