Do you need to compute in real-time or in batch? Noisy differentiation/integration is a specialty of mine.
Lots of possible approaches. If you have a good approx. of the amplitude, you should be able to clear a linear least squares param est
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iow, if you have y = A*sin(kx+b), and a good estimate for A, then perform LLS on kx_i+b = asin(y_i/A) for some N samples.
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Basically solve the system M [k b]^T = Y using standard LLS algorithm, [k b]^T = inv(M^T M) y, but can do better than computing inv.
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That solution will essentially be optimal if the noise characteristic is Gaussian and if the algorithm is fast enough.
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QAM in practice needs to be faster, so those algorithms generally operate directly in freq domain, less familiar with those
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Yeah, signal processing generally throws a lot of prerequisite crap at you, even though ultimately the implementation math is simple
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