What is the Savitzky-Golay 2nd derivative method?

[Another]

TL;DR

How are Savitzky–Golay second derivative different from Savitzky–Golay smoothing?

How are Savitzky–Golay second derivative different from Savitzky–Golay smoothing?

 

[jasonRF]

Assume we have a noisy data set with $N$ data points, $x_i$, where $i = 1, \ldots, N$.

Then Savitsky-Golay smoothing is equivalent to locally fitting a polynomial about each $x_i$ (using some number of neighboring data points), then evaluating that polynomial to produce a new $y_i$.

Savitsky-Golay differentiation is equivalent to locally fitting a polynomial about each $x_i$ (using some number of neighboring data points), then evaluating a derivative of that polynomial to produce a new $z_i$. This is of course only interesting to do if the order of the derivative is less than the order of the polynomial used in the fitting.

jason