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I have an input signal (blue) and a mean signal (green) which I compute from from previous signals). They looks like this:

diverge.png

(I also have the standard deviation signal and can do others if needed.)

From these signals I whish to clearly visualize two things:

  1. Short dips like the one pointed to by the arrow above; and
  2. Longer reduction in amplitude, say a 20% decrease in one period or more.

I've tried applying various functions to the difference between the two signals (Hilbert transformation among other things) but the oscillations make the curve hard to read, especially when zooming out. It's fair to assume the amplitude of the oscillations are pretty linear to the mean of the signal, as you probably can tell by just looking at the curves.

Is it possible filter out the noise but keep the short dips?

PS. I'm not too versed in math and would much appreciate a layman explanation alongside more stringent formulae.

Eric Wofsey
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Jonas Byström
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  • You need to better carachterize what you are looking for: from what I can understand in this post you can just filter out the points touching the red line or the points for which the signal is x units under its mean... but this could not be a good hint for the feature you are searching. – N74 Aug 22 '16 at 08:37
  • @N74: Touching the red line, zero, is not a good indicator if the signal naturally moves close to zero. Sometimes almost all samples of the signal is under the mean, but the local average of the input signal is just 10% below the local average of the mean signal. – Jonas Byström Aug 22 '16 at 08:44
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    So... how you find one such of these peaks, what is the process that makes you think that it must be marked? – N74 Aug 22 '16 at 08:50
  • The green doesn't really look like a mean signal. It rises above the mean values in quite some places. – mathreadler Aug 22 '16 at 10:23
  • You could do a wavelet thresholding or "shrinkage". Those were popular to do kind of the same things for pictures (images) some 15 years ago or so. Maybe it is a bit overkill, but depends a lot on what the signals and the noise can look like. – mathreadler Aug 22 '16 at 10:25

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