Complex representation of a signal, quadrature signals in receivers

In summary, the conversation discusses confusion with understanding complex signals and moving between physical signals and mathematical models. A real received signal can be represented by Euler's formula and can be split into two signals with a phase shift. The conversation also includes questions about symmetrical signals, the purpose of quadrature signals, and interpreting non-symmetrical signals. The person is seeking clarification and a concrete understanding of these concepts.
  • #1
luislandry
3
0
Hey, 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.
 
Engineering news on Phys.org
  • #2
Bump...any DSP guys want to chime in?

Possibly this could be moved into homework? It's not homework, but it could fit in there.
 
Last edited:

FAQ: Complex representation of a signal, quadrature signals in receivers

1. What is a complex representation of a signal?

A complex representation of a signal is a mathematical representation that uses complex numbers to represent the amplitude and phase of a signal. It is often used in signal processing and communication systems to simplify calculations and analysis.

2. How are quadrature signals used in receivers?

Quadrature signals, also known as IQ signals, are used in receivers to demodulate and process signals. They consist of two signals that are 90 degrees out of phase with each other, allowing for the separation of in-phase and quadrature components of the original signal.

3. What is the difference between in-phase and quadrature components?

In-phase components refer to the real part of a complex signal, while quadrature components refer to the imaginary part. In-phase components determine the amplitude of the signal, while quadrature components determine the phase.

4. How does a receiver use complex representation to improve signal processing?

A receiver uses complex representation to simplify and improve signal processing by converting the original signal into its in-phase and quadrature components. This allows for more efficient processing and demodulation of the signal.

5. Are there any limitations to using complex representation of a signal in receivers?

While complex representation can greatly improve signal processing and demodulation, it does have some limitations. It requires additional hardware and increases computational complexity, which can be a challenge for some systems. Additionally, it may introduce errors and inaccuracies in the demodulated signal if not implemented correctly.

Back
Top