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I am interested in removing oscillations from a signal to capture the lower-frequency variations, similar to the objective of this problem. The oscillations vary in frequency in the time domain, so wavelet shrinkage seems to be a reasonable option, but most of the literature on wavelet shrinkage is applied to denoising, where the noise to be shrunk is i.i.d. Gaussian. Low-frequency oscillations are generally autocorrelated.

Is it still technically sound to apply wavelet shrinkage for removing higher frequency components even though they are not noise? Is there a better method? I am not aware of too many spatially-adaptive low-pass filters which have a convenient interpretation as wavelets.

Below are examples of two of such signals. As you can see, the oscillations occur with different frequencies along the space/time domain (x-axis). I have tried Fourier smoothing, but it does not seem to leave any relevant features. (I have also tried truncated SVD, but it also does a horrible job removing the oscillations.)

enter image description here

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  • $\begingroup$ What's wrong with using the answer suggested in the post you point to? Jumping from there to wavelet shrinkage seems like a big leap. Can you share something of how your data looks? Can you do some stock standard filtering to precondition the signal before adding more complexity? $\endgroup$ – Peter K. Mar 22 '14 at 17:33
  • $\begingroup$ @Peter, thanks for the suggestion. I have added a figure to further illustrate my problem. $\endgroup$ – hatmatrix Mar 24 '14 at 10:45
  • $\begingroup$ Hey my friend, here some appreciations..... Somebody is asking you to put Wavelets, SVDs or Adaptive Low Pass Dynamic Non-linear Time-Varying Filters on the game?. Are you seeking for techniques for your PhD or Master Paper/Thesiswork, or is a problem you need readily solved?. Which features do you want to capture? Did you tried smooth or butter first than any other? Did you tried an spectrogram? Did you tried standard low pass filters? Did you tried the filter on the derivative?..... Answer me that for clarifying where to point this..... $\endgroup$ – Brethlosze Nov 4 '16 at 23:53

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