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Re: [Discuss-gnuradio] Visualizing Amplitude spectrum instead of power s


From: Fernando
Subject: Re: [Discuss-gnuradio] Visualizing Amplitude spectrum instead of power spectrum
Date: Wed, 26 Apr 2017 15:47:39 +0200
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.6.0

Hi!.

I think the amplitude spectrum is the DFT:


So, it has sign. The power spectrum is the absolute value so it has no sign.


I wish to be able to see the difference in the spectrum between this two signals below.  If the signal generators are A and B, A+B and A-B are different signals, but in the power spectrum we see them as the same signal, so I woul like to be able to difference one from the other from their spectrum.




regards




El 26/04/17 a las 09:52, Marcus Müller escribió:

Hey Fernando,

not quite sure I get what you need; I'd say the Amplitude Spectrum you'd be looking for is

$$A_{|\cdot|}[f]=|X[f]| = \left\lvert\sum_{n=0}^{N-1}
          x[n]\cdot e^{j2\pi \frac {nf}N}\right\rvert $$

or, rather, the decibel representation of that. There's no way to get a negative number out of the absolute of something – it's by definition a positive real number.

Now, we could also use our freedoms to define our amplitude spectrum to take the shape

$$A_\text{signed} = s(X[f]) |X[f]|\text{ with }
          s(X[f])=\begin{cases}1&\text{for } -\pi \le \angle X[f]
          < \pi \\ 0 &\text{else.} \end{cases}$$

But: that's really only useful if you have phase-coherent reception – as an analytic tool for an unsynchronized observation of the spectrum, it doesn't help you much, since you have a random $\angle$ due to having random relative phase.

So, maybe it'd be a good idea to formulate what purpose you're doing this for :) You can, indeed, tell 180° out-of-phase signals apart by this, but I'd argue that being 180° out-of-phase, for the most things I can think of, is only meaningful on one and the same frequency – and hence, I'm not quite sure this is what you're looking for!

Best regards,

Marcus


On 25.04.2017 12:01, Fernando wrote:
Hello.

Yes, with Time sink I can see the difference, but if the signal is compound of some other signals (for instance  signal=1K/amplitude +1 +2K/amplitude -1 +3K/qamplitude +1 +4K/amplitude +1 )  i would like to see the 2k signal as -1 amplitude, but in the power spectrum it will appear as possitive and in the QT time sink it is very difficult to see the signal as it is a complex one.

regards


El 25/04/17 a las 10:57, Jinyang Lee escribió:
Hello Fernando,

I think the QT GUI time sink displays the relationship between time and amplitude. You can see the signal through it. But when I use the channel model block,the QT2 can see the signal which is zero.
Enclose is running result with channel model and with channel model.

Regards,
Lee

2017-04-25 15:45 GMT+08:00 Fernando <address@hidden>:
Hi.


Is there a way of visualizing ampitude spectrum (with + and - signals)
instead of power spectrum?


regards



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