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speedracer
Joined: 29 Sep 2002
Posts: 23
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 20 May 2004 15:38 spectal inversion |
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hi! all,
i would like to know how i can demodulate a QAM signal while the spectrum is inverted due to mixing process?
i can extract both i channel and q channel fine, but the receiver needs to reverse the spectrum somehow.
thanx!
speedracer
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zorro
Joined: 06 Sep 2001
Posts: 319
Helped: 34
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| 20 May 2004 17:40 Re: spectal inversion |
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Hi speedracer,
it is not necessary to reverse the spectrum. You can process the inverted spectrum, just taking into account that the phases are changed in its signs. For instance, a phase change of +90 degrees in the noninverted spectrum corresponds to a phase change of -90 degrees in the inverted spectrum, and conversely.
You invert the spectrum (change from inverted/noninverted) conjugating the complex quantities:
Change the sign of the Q channel and you get a spectral inversion.
Change the sign of the I channel and you get a spectral inversion plus a sign change (180 degrees rotation).
Instead of inverting the Q channel you could consider the complex-conjugated constellation in the decoding process, but it seems to be "cleaner" (for clarity and maintenability) to invert Q in the digital processing.
Regards
Z
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speedracer
Joined: 29 Sep 2002
Posts: 23
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| 23 May 2004 4:52 Re: spectal inversion |
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hi! zorror,
i am wondering how one can mathematically prove by swapping I and Q and multiply -1 to Q, the spectrum can be reversed back.
Thanks!
speedracer
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zorro
Joined: 06 Sep 2001
Posts: 319
Helped: 34
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| 24 May 2004 19:01 Re: spectal inversion |
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Hi speedracer,
It is a mathematical property of Fourier transforms.
In what follows, the integrals extend over al the real axis;
P stands for PI
* stands for complex conjugated
The Fourier Transform of x(t) is X(f)=integ[x(t)exp(-j2Pft)dt]
The Fourier Transform of x*(t) is
integ{x*(t)exp(-j2Pft)dt} =
integ{x*(t)[exp(j2Pft)]*dt} =
integ{[(x(t)exp(j2Pft)dt]*} =
{integ[(x(t)exp(j2Pft)dt]}* = X*(-f)
The reversed spectrum is X*(-f), so the reversed spectrum in frequency domain corresponds to conjugation in time domain.
I hope this is clear. Regards
Z
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