Dear Enrico,
it would be helpful to see one of your spectra so to better understand the problem. Anyway, a good hint that you're monitoring enough slow frequency is the fact that your semicircles close on the real (X) axis, or, in other words, that the immaginary part of your data become negligible. Same idea is still valid for high frequency limit, but here is more difficult (you will always see higher frequency contributions).
Best regards,
Jacopo Remondina