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Dirak function

  1. Feb 5, 2004 #1
    hi,
    I would like to know why dirak-delta function is used in autocorrelation in a way that the following is true:

    <å(t)å(t')>=2Dä(t-t')

    where å(t)is Gaussian white noise and D is the strength of the noise.

    Dora
     
  2. jcsd
  3. Feb 6, 2004 #2
    I'm not familiar with the application that you are describing.

    One thing that you should mind is that the Dirac delta is not a function, but a distribution. It is the limit of a sequence of functions of area one, that are centered around a single point, and who's peak increases in the sequence. It can be seen as a "function" that is zero everywhere except for one point, and whose integral of the entire domain yields 1.
     
  4. Feb 6, 2004 #3

    selfAdjoint

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    This means that the white noise, being uncorrelated, cancels out between two different times, and only gives a D-value when the times coincide. You have [tex]\int f(t)\delta(a - t)dt = F(a)[/tex], where F is the antiderivative of f.
     
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