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IEVref: | 103-09-06 | ID: | |

Language: | en | Status: Standard | |

Term: | correlation function | ||

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Definition: | - function $f(t)$ which is a measure of the similarity of two deterministic functions ${f}_{1}(t)$ and ${f}_{2}(t)$, defined by
$f(t)={\displaystyle {\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}{f}_{1}}(\tau ){f}_{2}(t+\tau )\mathrm{d}\tau$ - function $f(t)$ which is a measure of the similarity of two stationary random functions ${f}_{1}(t)$ and ${f}_{2}(t)$, defined by
$f(t)=\underset{T\to \infty}{\text{lim}}\frac{1}{2T}{\displaystyle {\int}_{\text{\hspace{0.05em}}-T}^{\text{\hspace{0.05em}}+T}{f}_{1}(\tau )}{f}_{2}(t+\tau )\mathrm{d}\tau$
Note 1 to entry: The Fourier transform of $f(t)$ is equal to the product of the conjugate of the Fourier transform of ${f}_{1}(t)$ and the Fourier transform of ${f}_{2}(t)$: $F(\omega )={F}_{1}^{\ast}\left(\omega \right){F}_{2}(\omega )$ | ||

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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- function $f(t)$ which is a measure of the similarity of two deterministic functions ${f}_{1}(t)$ and ${f}_{2}(t)$, defined by
$f(t)={\displaystyle {\int}_{\text{\hspace{0.05em}}-\infty}^{\text{\hspace{0.05em}}+\infty}{f}_{1}}(\tau ){f}_{2}(t+\tau )\mathrm{d}\tau$

- function $f(t)$ which is a measure of the similarity of two stationary random functions ${f}_{1}(t)$ and ${f}_{2}(t)$, defined by
$f(t)=\underset{T\to \infty}{\text{lim}}\frac{1}{2T}{\displaystyle {\int}_{\text{\hspace{0.05em}}-T}^{\text{\hspace{0.05em}}+T}{f}_{1}(\tau )}{f}_{2}(t+\tau )\mathrm{d}\tau$

Note 1 to entry: The Fourier transform of $f(t)$ is equal to the product of the conjugate of the Fourier transform of ${f}_{1}(t)$ and the Fourier transform of ${f}_{2}(t)$:

$F(\omega )={F}_{1}^{\ast}\left(\omega \right){F}_{2}(\omega )$