I have radio telescope observations that have resulted in two real-valued signals (corresponding to the right- and left-handed circular polarizations).
The signals are sampled at rate $2B$, and provide a bandwidth of $B$.
I wish to get the full Stokes parameters from these signals, which requires me to convert these real signals into complex signals sampled at $B$ (half that of the real signals).
However, I don't know the procedure to do this. I just know that it is possible.
In general, how do I take a real-valued baseband signal and convert it to a complex-valued signal?