# Dirak function

1. Feb 5, 2004

### dora

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. Feb 6, 2004

### Kalimaa23

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.

3. Feb 6, 2004

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 $$\int f(t)\delta(a - t)dt = F(a)$$, where F is the antiderivative of f.