If I have an arbitrary time domain signal (e.g. a simple cosine) i can sample it with an ADC and get a time discrete representation. I can perform an FFT on the samples and get a complex output. The phase of the signal is:
Using an IQ down modulation of the same signal gives complex data, too, with the phase being:
Is there a difference between these two and when is one preferred over the other?
Thanks for the input!
@Dilip Sarwate: Here is what I did: set $\phi=60°$ (see your example)
The results are exactly what I expected. I can see the frequency of 1 Hz in the spectrum (plot 3) and the initial phase of $60°$ in the phase spectrum (plot 4). I get the same result when I use a non-complex function, e.g. $x(t)=cos(2\pi t+\phi)$.
I read everywhere that phase information is lost if I don't use IQ down-modulation, but that does not seem to be the case, as I can see the phase information in the plots.
Or am I missing something here?