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Computing a local smoothed numerical integration of a data set

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Deepayan Bhadra
Deepayan Bhadra 2014-3-10
编辑： Jan 2014-3-10
Hello,
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
Jan 2014-3-10
编辑：Jan 2014-3-10
You cannot obtain the original signal from the smoothed one. The smoothing destroys the noise information.

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Deepayan Bhadra
Deepayan Bhadra 2014-3-10
Hello Jan,
Say I calculate the numerical derivative without smoothing. Is there any method in that case?
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Jan
Jan 2014-3-10
编辑：Jan 2014-3-10
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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