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Area Mathematics - Functions / Spectrum

IEV ref103-09-07

en
autocorrelation function
  1. for a deterministic function, correlation function of the function and a time-delayed replica
  2. for a stationary random function, mathematical expectation of the product of the function and a time-delayed replica:

    C(t)=E[f(τ)f(t+τ)] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeacaGGOaGaam iDaiaacMcacqGH9aqpcaWGfbqcLbyacaGGBbGccaWGMbGaaiikaiab es8a0jaacMcacaaMc8UaamOzaiaacIcacaWG0bGaey4kaSIaeqiXdq NaaiykaKqzagGaaiyxaaaa@495C@

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)= lim T 1 2T T +T f(τ)f(t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeacaGGOaGaam iDaiaacMcacqGH9aqpdaWfqaqaaKqzGeGaaeiBaKqzaeGaaeyAaiaa b2gaaSqaaiaadsfacqGHsgIRcqGHEisPaeqaaOWaaSaaaeaajugabi aaigdaaOqaaKqzaeGaaGOmaOGaamivaaaadaWdXaqaaiaadAgacaGG OaGaeqiXdqNaaiykaiaadAgacaGGOaGaamiDaiabgUcaRiabes8a0j aacMcajugabiGacsgakiabes8a0bWcbaGaaGjcVlabgkHiTiaadsfa aeaacaaMi8Uaey4kaSIaamivaaqdcqGHRiI8aaaa@5AE8@


fr
fonction d'autocorrélation, f
  1. pour une fonction déterministe, fonction de corrélation de cette fonction et d'une version retardée de celle-ci
  2. pour une fonction aléatoire stationnaire, espérance mathématique du produit de la fonction par une version retardée de celle-ci:

    C(t)=E[f(τ)f(t+τ)] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeacaGGOaGaam iDaiaacMcacqGH9aqpcaWGfbqcLbyacaGGBbGccaWGMbGaaiikaiab es8a0jaacMcacaaMc8UaamOzaiaacIcacaWG0bGaey4kaSIaeqiXdq NaaiykaKqzagGaaiyxaaaa@495C@

Note 1 à l'article: La fonction d'autocorrélation d'une fonction déterministe ou d'une fonction aléatoire stationnaire est la transformée de Fourier inverse de sa densité spectrale de puissance.

Note 2 à l'article: Lorsqu'une fonction aléatoire stationnaire peut être considérée comme ergodique, sa fonction d'autocorrélation peut être calculée à partir d'une réalisation particulière:

C(t)= lim T 1 2T T +T f(τ)f(t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadoeacaGGOaGaam iDaiaacMcacqGH9aqpdaWfqaqaaKqzGeGaaeiBaKqzaeGaaeyAaiaa b2gaaSqaaiaadsfacqGHsgIRcqGHEisPaeqaaOWaaSaaaeaajugabi aaigdaaOqaaKqzaeGaaGOmaOGaamivaaaadaWdXaqaaiaadAgacaGG OaGaeqiXdqNaaiykaiaadAgacaGGOaGaamiDaiabgUcaRiabes8a0j aacMcajugabiGacsgakiabes8a0bWcbaGaaGjcVlabgkHiTiaadsfa aeaacaaMi8Uaey4kaSIaamivaaqdcqGHRiI8aaaa@5AE8@


ar
دالة الارتباط الذاتية

de
Autokorrelationsfunktion, f

es
función de autocorrelación

it
funzione di autocorrelazione

ja
自己相関関数

pl
funkcja autokorelacji

pt
função de autocorrelação

sr
аутокорелациона функција, ж јд

sv
autokorrelationsfunktion

zh
自相关函数

Publication date: 2009-12
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