Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dirak function

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


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

  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


    User Avatar
    Staff Emeritus
    Gold Member
    Dearly Missed

    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.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Dirak function
  1. Function for Gravity (Replies: 5)

  2. Partition function (Replies: 2)

  3. Green function (Replies: 2)

  4. State function (Replies: 10)