Thank you for your response! Let me see if I understood it correctly. If I apply dtft to a periodic signal, I should get an infinite frequency spectrum with only a finite number of frequencies having non-zero values, while the remaining ones will all be zero. Is that correct? If that's the case what would then be the consequence if I applied a DFT to an aperiodic signal? Will I simply be missing some information about the frequency domain?
Another thing, by time limiting the signal do you mean to simply not have an infinitely long signal? But aren't all signals we ever obtain finite?
Lastly, when should I use dtft instead of dft? Related to this, in many books showing, say, how to calculate coherence between two signals, they always use dtft in calculating spectra and cross-spectra. Is this just being more general, or is there a problem if I used dft instead for the same thing?