How to calculate the derivative of a discrete signal?

Question

Signal processing

I'm trying to reproduce the results of a signal processing publication.

The signal energy defined a general level of head movements.
After differentiating and taking the absolute value, we
computed the signal energy E(x) of each sample t using
E(t) = w_transposed * t

I divide the signal into different intervals of 1s. How to differentiate this signal now?
The signal is the accelerometer values ​​at certain intervals (100 readings per second)

Answer 1

Alternatively, you can consider the derivative as described in the Aerospace Science Journal. MSTU im. N.E. Bauman ( Elektron. zhur. 2016. No 04. P. 1–12.DOI:10.7463/a... )
By the way, the least squares method over several samples gives a more decent result for a noisy signal.