Numerical differentiation for an equi-spaced one-dim array. Five-point numerical differentiating using local cubic polynomial fit.
For more information, see
YangQuan Chen (2021). nd5p.m (https://www.mathworks.com/matlabcentral/fileexchange/3515-nd5p-m), MATLAB Central File Exchange. Retrieved .
A generalized framework called MaxPol has been recently published and made available here
MaxPol provides a framework to design variety of numerical differentiation kernels with properties like:
(1) Cutoff (lowpass) design with no side-lob artifacts (for noise-robust case)
(2) Arbitrary order of differentiation
(3) Arbitrary polynomial accuracy
(4) Derivative matrix design
(5) 2D Derivative Kernels with Steering moments
(6) Intuitive examples in Signal and Image processing
I programmed this in Mathcad and used it to differentiate some earthquake time-histories. Gave very good results. Thanks to Dr. Chen.
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