GENERAL LEAST-SQUARES SMOOTHING AND DIFFERENTIATION BY THE CONVOLUTION (SAVITZKY-GOLAY) METHOD

Smoothing and differentiation of large data sets by plecewlse least-squares polynomial fitting are now widely used techniques. The calculation speed Is very greatly enhanced if a convolution formalism is used to perform the calculations. Previously tables of convolution weights for the center-point least-squares evaluation of 2m + 1 points have been presented. A major drawback of the technique Is that the end points of the data sets are lost (2m points for a 2m + 1 point fitter). Convolution weights have also been presented in the special case of Initial-point values. In this paper a simple general procedure for calculating the convolution weights at all positions, for all polynomial orders, all filter lengths, and any derivative is presented. The method, based on the recursive properties of Gram polynomials, enables the convolution technique to be extended to cover all points in the spectrum. © 1990, American Chemical Society. All rights reserved.