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I have a discrete signal (vector of numbers) coming from a measurement. This signal has been filtered so that the noise has been removed. Now I am looking for an analytical representation of the signal (don't know if it is correct expression, I mean an analytical function that approximates the signal). My idea is to define an interpolation maybe using a spline. Any idea of how I can extract nodes from the vector to define a spline with a specific approximation? Can I consider the second (numerical) derivative as an estimation of the oscillation?

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    $\begingroup$ The answer depends a 100% on your signal and on what exactly you mean by "approximate". $\endgroup$ – Matt L. Nov 26 '19 at 13:03
  • $\begingroup$ I mean a curve that is as close as possible to the signal. $\endgroup$ – drSlump Nov 26 '19 at 13:16
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    $\begingroup$ I know that meaning of "approximate". The question is, what is your measure of "as close as possible"? $\endgroup$ – Matt L. Nov 26 '19 at 13:18
  • $\begingroup$ I don't have it. My idea is to set a threshold for the second derivative and catch the points above the threshold for the interpolation. After I can calculate the norm of the maximum error between the curves to have a value $\endgroup$ – drSlump Nov 26 '19 at 13:34
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    $\begingroup$ I think you need to give more information about the nature of the signal, specifically the "oscillation" you refer to. Are you saying that you have a signal whose salient feature is a sinusoidal component? What information are you trying to extract? If there's not a sinusoidal component, what do you expect to be there? $\endgroup$ – TimWescott Nov 26 '19 at 16:18

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