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IEVref:103-09-07ID:
Language:enStatus: Standard
Term: autocorrelation function
Synonym1:
Synonym2:
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Definition:
  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@


Publication date:2009-12
Source:
Replaces:
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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