# Second (numerical) derivative as estimation of oscillation

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?

• The answer depends a 100% on your signal and on what exactly you mean by "approximate". Nov 26 '19 at 13:03
• I mean a curve that is as close as possible to the signal. Nov 26 '19 at 13:16
• I know that meaning of "approximate". The question is, what is your measure of "as close as possible"? Nov 26 '19 at 13:18
• 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 Nov 26 '19 at 13:34
• 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? Nov 26 '19 at 16:18