Generalized Gans—Gill Method for Smoothing and Differentiation of Composite Profiles in Practice

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Abstract
A comparison has been made of the effectiveness of smoothing and differentiating Savitzky-Golay filters in terms of the minimization of total error criterion. The advantages of multipassing filters based on quartic/quintic (for smoothing) and cubic/quartic (for differentiation) polynomials have been proved. A generalized method is proposed for the choice of polynomial length, for both smoothing and differentiating filters, in the fine-structure analysis of composite spectra. This method follows the suggestion of P. Gans and G. B. Gill to locate an inflection point on the curve of variance of residuals between observed and smoothed spectra with respect to the polynomial length of the filter applied. A block diagram of the computer program is shown for optimum choice of polynomial lengths, and an example of its application in the analysis of the fine structure of an experimental multiplet band system is demonstrated.