Publication record · 18.cifr/1964.savitzky.sg-filter

Smoothing and Differentiation of Data by Simplified Least Squares Procedures.

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Abraham Savitzky (Perkin-Elmer Corporation), M. J. E. Golay (Perkin-Elmer Corporation)

RAI18.cifr/1964.savitzky.sg-filter

Analytical Chemistry· 1964· doi:10.1021/ac60214a047

A least squares method is presented for smoothing and differentiating spectroscopic data by convolving them with sets of integers (convolution integers) which are derived by fitting polynomials to successive groups of points. Tables of convolution integers are given for polynomials of degree 2 through 5 and for various window widths.

smoothingdifferentiationleast squaresconvolutionspectroscopysignal processing

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Analytical chemists needed to smooth noisy spectral/chromatographic data and compute derivatives for peak detection without distorting peak shapes. Moving-average methods degraded resolution; full least-squares fits were too slow for real-time use. Savitzky-Golay provided exact pre-computable convolution weights that preserve peak heights and widths.

Novelty

Savitzky and Golay derived closed-form convolution coefficients for least-squares polynomial fitting within a sliding window, making real-time smoothing and differentiation of spectral data computationally tractable. They pre-tabulated integer convolution weights for all practically useful window sizes and polynomial orders, unifying smoothing and differentiation in a single framework.

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