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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 


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