what is the principle of the function "diffnc" in /python/dmp/Trajectory.py about dmpbbo HOT 2 CLOSED

Numerical differentiation can be implemented as linear convolution. In Matlab for instance, diff(X) is basically the same as conv(X,[1,-1]). If you know the sample interval dt, it would be diff(X)/dt and conv(X,[1,-1]/dt)

https://bugra.github.io/work/notes/2014-06-13/first-second-derivative-convolution-quadratic-fitting-and-all-that-via-MCMC/#Taking-Derivatives-through-convolution

diffnc (as originally implemented by Stefan Schaal in Matlab, see the comments) works the same, but also smooths the signal by taking both neighbouring samples into account, i.e. conv(X,[1,0,-1]/2*dt)

diffnc is essentially a "minimal" version of this
https://en.wikipedia.org/wiki/Savitzky%E2%80%93Golay_filter
with m=3 and k=1.

In Python it would perhaps be more sensible to use numpy.gradient. But I copied diffnc from previous Matlab code I was using to ensure the result would be the same.

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I got it. Thank you

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