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Given the following signal, I would like to keep only the deceleration phase in orange.

enter image description here

I have no idea whether there exists techniques to do that or not. I imagine that I can smooth the signal, compute its derivative. But, I am not sure how to decide correctly when to cut the signal. In a perfect world, I would just consider the sign of the derivatives, but in ours, the smoothing may lead to some random punctual acceleration phases that are negligible in the deceleration phase. That makes the problem more difficult...

Any help will be appreciated ! Thanks.

N.B. I would like to add that I cannot filter using thresholds as I have to process several signals looking like this one but remaining different. I can try to do some statistics but I would like to know if there is signal processing based method that can deal with this problem efficiently.

EDIT Every signals I have slightly differ in the way they decreases (see derivatives amplitudes) and thus the time it takes for them to reach the low level you can see on the right side of the above curve.

I smoothed each signal using a Savitzky-Golay filter with the following parameter :

  • window size : 31
  • polynomial order : 3

This enables me to find a trade-off for smoothing my signals. Precisely, I smoothed the signals from the tip as suggested. Given those smoothed signals, I am able to compute nice first order derivatives and look at their sign. As a result, I am able to isolate the deceleration phase for all of them. But, my concern is about the methodology I used so far. Do you think it is a reasonable/good way to proceed ? I am wondering whether there are signal processing techniques that showed efficiency in this kind of problem. If so, it would be wise to use them :)

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  • $\begingroup$ start at tip, end at 90% to the endlevel $\endgroup$
    – tobalt
    Nov 4, 2021 at 16:37
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    $\begingroup$ Can you model the signal? Do you know what's the same and what's different about the various signals that you want to analyze? How much of that falling portion do you need to capture? There are an infinite number of ways to match your verbal description -- how many of them will actually do what you want? $\endgroup$
    – TimWescott
    Nov 5, 2021 at 3:15
  • $\begingroup$ @TimWescott don't hesitate to tell me if you want more explanations. $\endgroup$
    – Mistapopo
    Nov 5, 2021 at 18:04

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Your question is pretty general, but here's some guidance:

  • Yes, smoothing and then taking the derivative should work.
  • For the peak, you could find the maximal value within some span, and declare a peak detected when that maximum doesn't change for half a span or whatever.
  • For the trough, you could do the same thing, although the span may need to be longer if that one single example you give is truly representative.

Overall -- if it works, it's reasonable. For this sort of thing you either do a precise model and then find the theoretical optimal detector, or you just do some seat of the pants engineering. If the seat of the pants method works, then you're done.

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