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

From: Bahn William L Civ USAFA/DFCS
Subject: RE: [Discuss-gnuradio] Recovering x(t) from IQ samples
Date: Thu, 16 Aug 2007 18:42:39 -0600

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.

> -----Original Message-----
> From: address@hidden
> [mailto:address@hidden On Behalf
> Of Bahn William L Civ USAFA/DFCS
> Sent: Thursday, August 16, 2007 5:57 PM
> To: address@hidden
> 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.
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