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Area Mathematics - Functions / Spectrum

IEV ref103-09-06

en
correlation function
  1. function f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ which is a measure of the similarity of two deterministic functions f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ and f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ , defined by

    f(t)= + f 1 (τ) f 2 (t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcacqGH9aqpdaWdXaqaaiaadAgadaWgaaWcbaqcLbqacaaI XaaaleqaaaqaaiaayIW7cqGHsislcqGHEisPaeaacaaMi8Uaey4kaS IaeyOhIukaniabgUIiYdGccaGGOaGaeqiXdqNaaiykaiaadAgadaWg aaWcbaqcLbqacaaIYaaaleqaaOGaaiikaiaadshacqGHRaWkcqaHep aDcaGGPaqcLbuaciGGKbGccqaHepaDaaa@53B2@

  2. function f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ which is a measure of the similarity of two stationary random functions f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ and f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ , defined by

    f(t)= lim T 1 2T T +T f 1 (τ) f 2 (t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcacqGH9aqpdaWfqaqaaKqzafGaaeiBaiaabMgacaqGTbaa leaacaWGubGaeyOKH4QaeyOhIukabeaakmaalaaabaqcLbuacaaIXa aakeaajugqbiaaikdakiaadsfaaaWaa8qmaeaacaWGMbWaaSbaaSqa aKqzaeGaaGymaaWcbeaakiaacIcacqaHepaDcaGGPaaaleaacaaMi8 UaeyOeI0IaamivaaqaaiaayIW7cqGHRaWkcaWGubaaniabgUIiYdGc caWGMbWaaSbaaSqaaKqzaeGaaGOmaaWcbeaakiaacIcacaWG0bGaey 4kaSIaeqiXdqNaaiykaKqzafGaciizaOGaeqiXdqhaaa@5E5D@

Note 1 to entry: The Fourier transform of f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ is equal to the product of the conjugate of the Fourier transform of f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ and the Fourier transform of f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ :

F(ω)= F 1 ( ω ) F 2 (ω) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeqyYdCNaaiykaiabg2da9iaadAeadaqhaaWcbaGaaGymaaqaaiabgEHiQaaakmaabmaabaGaeqyYdChacaGLOaGaayzkaaGaamOramaaBaaaleaajugWaiaaikdaaSqabaGccaGGOaGaeqyYdCNaaiykaaaa@4664@


fr
fonction de corrélation, f
  1. fonction f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ mesurant la similitude de deux fonctions déterministes f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ et f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ , définie par

    f(t)= + f 1 (τ) f 2 (t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcacqGH9aqpdaWdXaqaaiaadAgadaWgaaWcbaqcLbqacaaI XaaaleqaaaqaaiaayIW7cqGHsislcqGHEisPaeaacaaMi8Uaey4kaS IaeyOhIukaniabgUIiYdGccaGGOaGaeqiXdqNaaiykaiaadAgadaWg aaWcbaqcLbqacaaIYaaaleqaaOGaaiikaiaadshacqGHRaWkcqaHep aDcaGGPaqcLbuaciGGKbGccqaHepaDaaa@53B2@

  2. fonction f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ mesurant la similitude de deux fonctions aléatoires stationnaires f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ et f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ , définie par

    f(t)= lim T 1 2T T +T f 1 (τ) f 2 (t+τ)dτ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcacqGH9aqpdaWfqaqaaKqzafGaaeiBaiaabMgacaqGTbaa leaacaWGubGaeyOKH4QaeyOhIukabeaakmaalaaabaqcLbuacaaIXa aakeaajugqbiaaikdakiaadsfaaaWaa8qmaeaacaWGMbWaaSbaaSqa aKqzaeGaaGymaaWcbeaakiaacIcacqaHepaDcaGGPaaaleaacaaMi8 UaeyOeI0IaamivaaqaaiaayIW7cqGHRaWkcaWGubaaniabgUIiYdGc caWGMbWaaSbaaSqaaKqzaeGaaGOmaaWcbeaakiaacIcacaWG0bGaey 4kaSIaeqiXdqNaaiykaKqzafGaciizaOGaeqiXdqhaaa@5E5D@

Note 1 à l'article: La transformée de Fourier de f(t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgacaGGOaGaam iDaiaacMcaaaa@388F@ est égale au produit de la conjuguée de la transformée de Fourier de f 1 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIXaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FA@ par la transformée de Fourier de f 2 (t) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba qcLbqacaaIYaaaleqaaOGaaiikaiaadshacaGGPaaaaa@39FB@ :

F(ω)= F 1 ( ω ) F 2 (ω) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHXgaruavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGeaGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaqFn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpeWZqaaiqaciWacmGadaGadeaabaGaaqaaaOqaaiaadAeacaGGOaGaeqyYdCNaaiykaiabg2da9iaadAeadaqhaaWcbaGaaGymaaqaaiabgEHiQaaakmaabmaabaGaeqyYdChacaGLOaGaayzkaaGaamOramaaBaaaleaajugWaiaaikdaaSqabaGccaGGOaGaeqyYdCNaaiykaaaa@4664@


ar
دالة الارتباط

de
Korrelationsfunktion, f

es
función de correlación

it
funzione di correlazione

ja
相関関数

pl
funkcja korelacji

pt
função de correlação

sr
корелациона функција, ж јд

sv
korrelationsfunktion

zh
相关函数

Publication date: 2009-12
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