# signal uncorrelated with delta in the origin

I have a stochastic process completely uncorrelated. Why the autocorrelation function has a delta of dirac in the origin? Which is the reason of that?

$R_{XX}({\tau})=A{\delta(\tau)}$

where $R_{XX}$ is the autocorrelation function of $X$ process and $A$ is a constant dependent by process spectrum

As you noted, the wide-sense stationary stochastic process $X(t)$ is uncorrelated with itself for all nonzero time lags $\tau$. For $\tau=0$, it's impossible for a process to be uncorrelated with itself (unless $X(t)$ is the trivial process $X(t)=0$). Look at the definition for $R_{XX}(\tau)$:
$$R_{XX}(\tau) = E(X(t)X^*(t+\tau)$$
$$R_{XX}(0) = E(|X(t)|^2)$$
By definition, $|X(t)|^2$ must be $\ge 0$, so its expectation must also satisfy that condition.