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## [Discuss-gnuradio] Recovering x(t) from IQ samples

**From**: |
Bahn William L Civ USAFA/DFCS |

**Subject**: |
[Discuss-gnuradio] Recovering x(t) from IQ samples |

**Date**: |
Thu, 16 Aug 2007 17:56:44 -0600 |

If my i(t) and q(t) samples are defined as follows:
i(t) = x(t) * sin(wt)
q(t) = x(t) * cos(wt)
then, given i(t) and q(t), I can recover the magnitude of x(t) as follows:
|x(t)| = sqrt(i^2(t) + q^2(t))
But how can I recover the sign of x(t)? For each of the four possible
combinations of the signs of i(t) and q(t), x(t) could be either positive or
negative.
Thanks.

**[Discuss-gnuradio] Recovering x(t) from IQ samples**,
*Bahn William L Civ USAFA/DFCS* **<=**
**RE: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Bahn William L Civ USAFA/DFCS*, `2007/08/16`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Johnathan Corgan*, `2007/08/17`
**RE: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Bahn William L Civ USAFA/DFCS*, `2007/08/17`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Jens Elsner*, `2007/08/18`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Jonathan P Jacky*, `2007/08/18`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Jeff Brower*, `2007/08/18`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Jonathan Jacky*, `2007/08/20`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Chris Stankevitz*, `2007/08/20`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Brian Padalino*, `2007/08/20`
**Re: [Discuss-gnuradio] Recovering x(t) from IQ samples**, *Jens Elsner*, `2007/08/18`