The Savitzky-Golay Filter is an often occurring data processing step in instrumental analytical chemistry. The following link presents a pretty straightforward explanation on the mathematical background involved. You will need knowledge of linear algebra...
http://www.vias.org/tmdatanaleng/cc_filter_savgol_math.html
A more detailed explanation with some sample code and spectral results are on this link:
http://www.ma.utexas.edu/documentation/nr/bookcpdf/c14-8.pdf
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