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I have several sequences with varying standard deviations, and I want to smooth them so that each sequence has approximately the same standard deviation, which I've predetermined.

I'm open to any method suggestions for achieving this. Can anyone provide guidance/resources on how to accomplish this?

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    $\begingroup$ Can you add more details about the properties of the sequences? The easiest would be just to try different lowpass filters and reduce the cutoff until you have the target standard deviation. However this may affect other "properties" of the signal. $\endgroup$
    – Hilmar
    Commented Apr 7 at 23:23

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One approach is to use the fact that the signal variance (which can be computed from the standard deviation) is equal to the signal power with its mean removed. Therefore:

  1. Remove the signal mean
  2. Transform to the frequency domain
  3. Remove all high frequency content that causes the power to exceed the threshold you're targeting
  4. Transform back to the time domain
  5. Add back the signal mean that you removed in step (1).

This will allow you to obtain the exact standard deviation you want using an ideal low pass filter.

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