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If I have a discrete real-time signal $x[n]$, with its latest value $x[i]$ and all its past values $x[i-t]$, how can I estimate the derivative at $x[i]$?

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  • $\begingroup$ One possibility might be fitting a smoothed (overdetermined) polynomial regression using several earlier points, and using the derivative of that polynomial as an estimate. $\endgroup$ – hotpaw2 Feb 24 '14 at 15:36
  • $\begingroup$ What kind of a signal are you working with? A little more information might help. $\endgroup$ – Amal Mar 23 '17 at 18:16
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Is the derivative between x[n] and x[n-1] useful enough, hence x'[n] = x[n] - x[n-1] ? Or do you need a better estimate?

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  • $\begingroup$ No, not useful enough, because in the next step I would like to do a derivative of the derivative and then the mistake adds up. Also the data is really "jumpy". Sometimes nothing happens and then there's a jump every now and then. So I always smooth the latest 4 values. $\endgroup$ – JustGoscha Feb 24 '14 at 11:17
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A reasonable solution in this case would be to do a curve fit and then establish an estimate of the derivative using the "smoothed" solution, which would help eliminate your noise issues.

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