Computing a local smoothed numerical integration of a data set

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?

Answer 1

[Jan]

You cannot obtain the original signal from the smoothed one. The smoothing destroys the noise information.

Answer 2

[Deepayan Bhadra]

Hello Jan,

Say I calculate the numerical derivative without smoothing. Is there any method in that case?

[Jan]

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.