Assume we have:
- real signal: $s(t)$
- its analytic representation: $s^+(t) = s(t) + j*H(t)$, where $H(t)$ - Hilbert transform of $s(t)$
Spectrum of $s^+(t)$ has only positive part, so may be sampled with frequency $f_p = F_n/2$ (without aliasing); where $F_n$ - Nyquist frequency for real signal. Its for example LTE20 case which IQ representation is sampled with $f_p=30.72MHz$.
The question is: how to restore real signal from analytic representation if sampled under $F_n$?
(Typical literature response is that just imaginary part can be discarded, but they silently assumes that $f_p >= F_n$.)