>>And about shape the
>>frequency spectrum of the subcarriers - I see that dependence is, but I
>>can not mathematicly describe it.

Well if there is no cyclic prefix, then it is a rectangular window =
rect(t). The fourier transform of this is sinc(f). So a single sub-
carrier of frequency f1 in the time domain multiplied by a rectangular
function, is a pair of impulses at +/- f1 in the frequency domain,
convolved with a sinc function.

> What length of a prefix should be if the interval between subcarriers is
> 100Hz?.
> And what length of a prefix should be if the interval between subcarriers
> is 60Hz?

I don't know the answer, but thinking out loud: If the time duration
(including cyclic prefix) of the OFDM symbol is T, and assuming a
rectangular window, then the main-lobe width of a single sub-carrier
in the frequency domain is 1/T. So I suppose the OFDM subcarriers
cannot be spaced any closer than 1/T Hz. So presumably it follows that
a longer cyclic prefix, allows the sub-carriers to be spaced closer
together.

But, my understanding is the cyclic prefix is shaped such that it
gives something other than a rectangular window to the OFDM symbol.
This means a sub-carrier main lobe width is now > 1/T, but the
advantage is the side lobes drop off with frequency at a faster rate,
and/or the first side lobe is reduced. So in this case the sub-
carriers must be spaced > 1/T.

Windowing trades off main lobe width vs side lobe height and roll off
rate. There are many different windows out there. Maybe there is a
particular type that often gets used for OFDM applications?

Disclaimer: I'm still learning about OFDM myself

Cheers
Andrew