Savitzky and Golay smoothing filters

12/24/2003

Savitzky and Golay Smoothing Filters

Original 1964 Analytical Chemistry article:
- Savitzky, A. and Golay, M.J.E.
- Smoothing and Differentiation of Data by Simplified Least Squares Procedures
- Analytical Chemistry 36(8):1627-1639, July 1964.
Numerical Recipes in C - chapter on Savitzky and Golay smoothing. The concise representation here is the source for the Lispix code.
- Press, W. H. et. al.
- Numerical Recipes in C, 2nd Ed.
- Cambridge U. Press, 1992.
- Available on line: http://www.numerical-recipes.com/nronline_switcher.html
Hints on how to use the filters.
- Bromba, M.U.A. and Ziegler, H. 1981.
- Applications Hints for Savitzky-Golay Digital Smoothing Filters
- Analytical Chemistry 53(11): 1583-1586.

Lispix implementation: s&g-coefs (nl nr m deriv)

nl - number of neighbors to left.
- In practise, use lots of neighbors, up to about the width of the peaks you desire.
- Full width of degree 4 filter should be between 1x and 2x FWHM of features you desire.
nr - number of neighbors to right
- (Points averaged = nl + nr + 1).
- nl + nr >= m.
m - order of smoothing poynomial.
- Usual values are 2, or 4 for quadratic or quartic.
- 0 is for simple averaging.
deriv, deriv <= m (m usually >= 4.)
- 0 - smoothing
- 1 - slope - 1st derivitive
- 2 - 2nd derivitive, etc.
In the Filter / variable buttons, nl = radius, nr = radius.