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5-point stencil or Savitsky-Golay for differences

Started by Unknown April 25, 2019
I had some code computing the second difference of a sampled signal as
(x(n-1)-2x(n)+x(n+1))/(square of interval)
I only needed a crude estimate of the second derivative in this case.

Then I came across "five point stencils"
By this method, the second difference is
(-x(n-2)+16x(n-1)-30n(n)+16x(n+1)-x(n+2))/12/(square of interval)

And then 5-sample Savitsky-Golay formula, which seems rather different
(2x(n-2)-x(n-1)+2x(n)-x(n+1)+2x(n+2))/7/(square of interval)

Are either of these "better" in any sense?
On Thursday, April 25, 2019 at 3:13:58 AM UTC-5, conr...@gmail.com wrote:

> I only needed a crude estimate of the second derivative in this case.
Not sure whether this will be helpful or not, but http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/ and http://www.holoborodko.com/pavel/wp-content/plugins/download-monitor/download.php?id=8
On Thursday, April 25, 2019 at 8:35:11 PM UTC+8, Greg Berchin wrote:
> > Not sure whether this will be helpful or not, but > http://www.holoborodko.com/pavel/numerical-methods/numerical-derivative/smooth-low-noise-differentiators/
Thanks for that reference. It seems the first formula was derived for a higher-order polynomial, explaining the different coefficients.