Let $f$ be a real function. Is there a connection between
- The first positive abscissa for which its autocorrelation function is equal to zero (which I call the first passage time, fpt)
- The largest frequency of $f$'s power spectrum
For the matter, we can assume $f$ infinitely differentiable, square-integrable and anything more if needed. I know the Wiener-Khinchin theorem relates autocorrelation to power spectrum, but I'm not sure how to go further.