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

[Bahn William L Civ USAFA/DFCS]

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.