I recently asked a question about fitting a sine wave with a distorted time base, and had some great answers at the following link: Fit sine wave with a distorted time-base
However, I would like to perform a similar fit, but now the signal is noisy. I assume I will have to do some normalisation between -1 and 1, and also remove the slow drift.
The original question is as follows:
I want to know the best way to fit a sine-wave with a distorted time base, in Matlab.
The distortion in time is given by a n-th order polynomial (n~10), of the form
t_distort = P(t).For example, consider the distortion
t_distort = 8 + 12t + 6t^2 + t^3(which is just the power series expansion of(t-2)^3).This will distort a sine-wave as follows:
I want to be able to find the distortion given this distorted sine-wave. (i.e. I want to find the function
t = G(t_distort), butt_distort = P(t)is unknown.)
Now instead of finding the distortion of a distorted sin-wave when it is perfectly normalised between -1 and 1 (and has no other distortion other than the time-base), I would like to find the distortion of a distorted sine-wave which is noisy and also has a drift. (N.B. I am not concerned with this drift at all, and preferably, it would be removed). Such a signal would be as follows:
