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Given the following signal I would like to calculate the rate of damping.

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I presume that I need to find out where the peaks are using some kind of smoothing on the sample data. After performing an FFT I get the following…

enter image description here

I guess I could perform some kind of clipping (high/low pass) and then do an inverse FFT to get the smoothed result.

Am I on the right track here? Are there some standard methods for achieving my goal?

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The simplest method would be to detect the local maxima and then fit an exponential on these points only. It would be a bit approximate because it looks like your data contains more than one exponentially damped sinusoid.

A more proper solution is to use Prony's method (or ESPRIT, MUSIC) - any parametric method fitting a "sum of exponentially damped sinusoids" model to your data.

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  • $\begingroup$ The thing is that I am only interested in the largest sinusoid. I would like to filter the others out so I can calculate the damping effect on this main sinusoid. Would I not need any filtering if I applied the Prony's method? $\endgroup$ – Onato Nov 8 '14 at 0:24
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    $\begingroup$ The point of these parametric methods is that they model a sum of damped sinusoids. In your example, there appears to be 3 of them; so the model will give you the frequency/damping rate of the 3 of them; and you won't need filtering. $\endgroup$ – pichenettes Nov 8 '14 at 9:30
  • $\begingroup$ The above data is just an example. I intend to write an app that will calculate the damping on real world sample data automatically. Do I understand correctly in that I would need some software like R or MatLab to fit an exponential to my data? $\endgroup$ – Onato Nov 8 '14 at 13:15
  • $\begingroup$ You can do it quickly with high level tools like R or matlab, but with a bit of work, the same algorithms used in these tools can be reimplemented in any programming language of your choice. $\endgroup$ – pichenettes Nov 8 '14 at 15:04

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