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Computing a local smoothed numerical integration of a data set

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I have a data set (pitch rate q_a) shown in blue. Using a standard SIDPAC code, I computed a local smoothed numerical time derivative (q_deriv in red). What command/code can help me recover the original data set q from q_deriv?

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Jan il 10 Mar 2014
Modificato: Jan il 10 Mar 2014
You cannot obtain the original signal from the smoothed one. The smoothing destroys the noise information.

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Deepayan Bhadra
Deepayan Bhadra il 10 Mar 2014
Hello Jan,
Say I calculate the numerical derivative without smoothing. Is there any method in that case?
  1 Commento
Jan il 10 Mar 2014
Modificato: Jan il 10 Mar 2014
Looks a a small example:
x = [9, 10]
Now calculate the derivative:
d = 1;
Finally a recontruction of the original signal is not possible, obviously.
But if you store the first value in addition, the reconstruction works again.

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