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IEVref: | 103-09-07 | ID: | |

Language: | en | Status: Standard | |

Term: | autocorrelation function | ||

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Definition: | - for a deterministic function, correlation function of the function and a time-delayed replica
- for a stationary random function, mathematical expectation of the product of the function and a time-delayed replica:
$C(t)=E[f(\tau )\text{\hspace{0.17em}}f(t+\tau )]$
Note 1 to entry: The autocorrelation function of a deterministic function or a stationary random function is the inverse Fourier transform of its power spectral density. Note 2 to entry: When a stationary random function can be considered as ergodic, its autocorrelation function can be calculated from a particular sample: $C(t)=\underset{T\to \infty}{\text{lim}}\frac{1}{2T}{\int}_{\text{\hspace{0.05em}}-T}^{\text{\hspace{0.05em}}+T}f(\tau )f(t+\tau )\mathrm{d}\tau$ | ||

Publication date: | 2009-12 | ||

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Internal notes: | 2017-02-20: Editorial revisions in accordance with the information provided in C00020 (IEV 103) - evaluation. JGO 2017-08-25: Removed <p> tag between <li> tags. LMO | ||

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- for a deterministic function, correlation function of the function and a time-delayed replica
- for a stationary random function, mathematical expectation of the product of the function and a time-delayed replica:
$C(t)=E[f(\tau )\text{\hspace{0.17em}}f(t+\tau )]$

Note 1 to entry: The autocorrelation function of a deterministic function or a stationary random function is the inverse Fourier transform of its power spectral density.

Note 2 to entry: When a stationary random function can be considered as ergodic, its autocorrelation function can be calculated from a particular sample:

$C(t)=\underset{T\to \infty}{\text{lim}}\frac{1}{2T}{\int}_{\text{\hspace{0.05em}}-T}^{\text{\hspace{0.05em}}+T}f(\tau )f(t+\tau )\mathrm{d}\tau$