Given a signal with zero mean and a standard deviation of 0.1 sampled at 5000 Hz.
What would be the Standard Deviation of its 1st, 2nd and 'n' derivative?
For instance, let's say we measure the distance to a constant range target. The STD of the sensor measurements of the range is 0.1 [Meter] (Assume the error is white) and its sampling rate is 5000 Hz.
What would be the standard deviation of the acceleration process?