How do I calculate a function if I know its auto-correlation?
To be more specific, I have a function of one variable, let's call it $g(x)$, and I know it's the cross-correlation of a function $f(x)$ with itself. In formulas $$ g(x)=\int_{-\infty}^{+\infty}f(t)f(x+t)dt $$ I want $f(x)$, how do I get it?
If possible, I would like to have an analytic answer. Otherwise, I actually have $g(x)$ sampled in a finite number of points, so a numeric procedure to derive $f(x)$ would also do the job.
Thanks!