# Homework Help: Complex representation of a signal, quadrature signals in receivers

1. Aug 13, 2010

### luislandry

(I posted this in the elctrical engineering forums because it's technically not homework, but it probably belongs here...it got no replies there)

I'm hoping this thread can clear up some confusion I have with complex signals and moving back and forth from physical signals to the mathematical models. I'll probably ask some questions specifically, but if you would like to help me please treat this whole post as a question because I'll try to walk through my understanding of the subject and it may be wrong in places.

A real received signal will have a form such as A*cos(wt + p). This can also be represented by Euler's formula by two complex sinusoids with additive inverse frequencies: A/2*exp(wt + p) + A/2*exp(-(wt + p)).

A receiver splits this into two signals and phase shifts one by 90 degrees, giving two signals A*cos(wt + p) and A*sin(wt + p), which are represented by A*exp(wt + p).

Q1: When a signal is shown in the frequency domain, and is symmetrical about the zero-frequency line, would this be the real signal?

Q2: When it is shown only in the positive frequencies, it's either just to save space on the diagram, or to represent the in-phase AND quadrature signals. Right?

Q3: What is the purpose of the quadrature signals? I didn't fully follow the explanations I've seen so far.

Q4: How do you interpret signals that are shown as not being symmetric about the zero-frequency line? How can these be realized as real signals?

Thanks a ton for your help here, I feel like these are details that I sort of glossed over before and would like a concrete understanding of.