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

 From: Jeff Brower Subject: Re: [Discuss-gnuradio] Recovering x(t) from IQ samples Date: Fri, 17 Aug 2007 11:00:24 -0500

```William-

> I supposed I can reconstruct a virtual local oscillator by looking at
> the zero crossings and syncing a sine generator to that and then using
> the sine generator to determine the sign (making it a sign generator ;-P).
> Then my entire waveform might be inverted, but that is probably not much
> of a concern (at least for my needs).
>
> Please tell me there is a better way.

If I recall, you're trying to use the USRP as a high speed data acquisition
board and
do some processing on another (external) FPGA or DSP board, is that correct?
With
which daughtercard?  If it's one of the basic daughtercards that doesn't
downshift,
then you could modify FPGA logic to not multiply I data.  I haven't looked
closely,
but it should be straightforward in the Verilog source to go around that step.

If you're using one of the daughtercards that downshifts prior to A/D then my
understanding is you have to deal with I-Q data.

-Jeff

> > -----Original Message-----
> > Of Bahn William L Civ USAFA/DFCS
> > Sent: Thursday, August 16, 2007 5:57 PM
> > Subject: [Discuss-gnuradio] Recovering x(t) from IQ samples
> >
> > 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.

```