What is a complex signal and how can you make one in real life?

[ltkenbo]

I'm in a discrete time signals class at my University and we talk about signals all the time that have imaginary portions. But I don't understand what this actually means in terms of a "real" life signal. I understand the relation to a vector spinning about the imaginary and real axis but what does this mean? How would I physically generate this type of signal?

 

[Mityan]

That is a mathematical abstraction very useful for system analyzis ans synthesis.
In real world over the communication channel the real signal without imaginary part is always transmitted. But you get your complex signal by multiplying it with two sinusoids shifted by pi/2 (i.e. sin & cos) and call these two multiplication results "real and imaginary parts" and process them together as a single complex signal with the appropriate arythmetics.

 

[ltkenbo]

But how does it help us in analysis? What is the advantage of using imaginary numbers. Like with a DTFT instead of a complex exponential/sinusoid why couldn't we use a strictly real sinusoid?

 

[RCinFLA]

The signal is presented in quadrature. Think of it as a phasor represented in cartesian coordinate form. One big advantage is usually when sinewave is passing through zero the cosine wave is peaking (and vise versa).

Easiest way to generate is by mixer downconverting where the two mixers are fed with quadrature local oscillator signal. The two quadrature LO signals are easily generated with frequency dividers. Other way to generate quadrature signal is from Hilbert transform.