Don't understand dirac delta function for white noise?

Question

Say we have stochastic differential equation

$\frac{dx}{dt} = n(t)$

where $n(t)$ is a noise process.

$n(t)$ has a correlation function $R(t - t') = <n(t)n(t')>$

If the noise process is white noise then we have

$<n(t)n(t')> = \delta(t - t')$

where $\delta$ is the dirac delta function.

I don't understand what this means? I would imagine it is supposed to imply that there is no correlation between the value of $n$ at $t$ and $t'$, simply because its called 'white noise'. But I don't see how the dirac delta function gives us that?

Answer 1

Correlation is an index to show how much shape of two functions are similar.

Ideal noise is similar to nothing. Otherwise it is not noise.

$<n(t),n(t')> = \delta(t - t')$

Means that if you shift a white noise it has zero correlation to itself. And if you don't shift it, it is identical to itself.