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The Savitzky-Golay algorithm is based on performing a least squares linear regression fit of a polynomial of degree k over at least k+1 data points around each point in the spectrum to smooth the data. The derivative is then the derivative of the fitted polynomial at each point. The calculation uses the matrix formalism described in Steiner, et. al. (see References) to calculate 1st through 9th derivatives. The calculation is performed with the data in low X to high X order. If the input trace goes from low to high, it is reversed for the calculation and then re-reversed afterwards.
Let:
d = the order of the derivative
k = the degree of the polynomial
s = the number of points to be fitted by the polynomial
m = (s-1)/2
P = An s-element array with values (-m,...,0,...+m)
 = A k-element array parameters
y = The array of actual spectral data points
Then y = X and the least squares fit is given by minimizing
 which is given by the condition: dS / dQ = 0.
This yields:
The dth derivative is then given by (d!) times the (d+1)th row of the T convolved with the trace data:
Note that this convolution truncates the trace by m points on each side. | 
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