I need to calculate the derivative from a list of experimental points. Mathematica has two functions which seem to do this: DifferentiatorFilter and DerivativeFilter. Which one is better for calculating a derivative? Is there one that implements a finite difference method?
From the documentation:
DifferentiatorFilter is commonly used to approximate the derivative of data. Data smoothing with cutoff frequency omega.
DerivativeFilter is a linear filter that computes the derivatives of data based on a spline interpolation model. Regularization with a Gaussian kernel of standard deviation [Sigma] (default value is [Sigma]=0) can be used to reduce susceptibility to noise.