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I have two periodic noisy signals which depend on a constantly increasing reference angle. The two signals are shifted by 90 degrees and one of them has an unknown varying offset. Two sample signals like this can be generated using a simple python code:

instantaneous_phase=np.linspace(0,6*np.pi,1000) % (2*np.pi)

unknown_offset=np.linspace(0,1,1000)

signal1=np.sin(instantaneous_phase) + ((np.random.rand(1000))-0.5)/10
signal2=np.cos(instantaneous_phase) + ((np.random.rand(1000))-0.5)/10 + unknown_offset

Giving something like:

enter image description here

I need to reconstruct instantaneous_phase, using only signal1 and signal2. Is this possible? I'd appreciate if someone can point me in the right direction.

Nickj
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  • When you say "determine quadrant", do you really mean "determine frequency/phase", or something like that? Can you clarify what's known, and what isn't known? – Oliver Charlesworth Dec 05 '17 at 14:32
  • Hi, Thanks for you comment. I updated the question title - hope it makes more sense now. Known parameters are `signal1` and `signal2`, unknown is `instantaneous_phase`, which I need to reconstruct. – Nickj Dec 06 '17 at 07:47

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