I have an algorithm which takes an input signal, $x[t]$, and (among other things) complex basebands the data and outputs the phase of the complex numbers.
I'm new to the field and the Matlab function which produces the basebanded signal is a kind of black box to me. I've tried reading the code, but it's pretty impenetrable and not commented. I also tried to input different shapes of signals, but couldn't learn much from it. My questions are:
What exactly is the complex baseband of a signal? I sort of understand what "baseband" means, but where does the complex phase come from?
Related, does the phase have any relation to the signal? If I input a sinusoid, what should I expect the phase output to be?