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I have this non-stationary signal. enter image description here

the mean is roughly constant but the second moment (autocorrelation) does not depend only on the time lag $tau$. Correct me if I am wrong in the above statement.

Anyway as you see I have high frequency noise components and I would like to clean it but avoiding any sort of phase lag introduced by a filter. What can I do to achive my purpose? I thought of using wavelets to extract the coefficients and then reconstruct the signal, but maybe there is a more efficient and correct way of doing it.

Can you also provide with a link/guide to code this in python?

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  1. Break your signal into short overlapping frames over which it is stationary. Say, the length of the frame is $L$ samples. You can window it to smooth out discontinuities. For example, you can use a Hann window with an overlap of $L/2$ samples.
  2. On each windowed frame, use the Wiener filter to find the optimal inverse filter coefficients to cancel your noise. See scipy.signal.wiener.
  3. Overlap add your filtered signal frames to recover the original non-stationary signal.
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