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.

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