Taking a Fourier-transform of a real signal, gives me a spectrum that has symmetry. If I take the FFT of a real signal, then throw away half of the spectrum, and then do an inverse transform I get a complex-signal. I go from r(t) to rc(t) where rc(t) is a complex-signal. Now this complex-signal supposedly contains all the information to reconstruct the original real-signal. My question is, how?