Direct Use of Second Derivatives in Curve-Fitting Procedures

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Abstract
Most curve-fitting procedures deal with an unknown, variable baseline by modeling it with a function involving a number of parameters. In view of the facts that (1) there is often no analytically relevant information in the baseline, and (2) there is usually no functional form known, a priori, for the baseline, we have chosen to eliminate it by means of the second-derivative transformation. The resulting profile is deconvoluted by fitting it with the second derivative of the sum of an appropriate number of component curves. The utility of this procedure is demonstrated on simulated data with typical baselines and noise levels, and on real FT-IR data. Peak parameters (such as position, width, and area) obtained from this technique are comparable to those obtained by fitting the original spectrum with Lorentzian curves and a simple baseline. The major advantage of this procedure is the reduction in the number of parameters that must be optimized in the fitting method. Applications of the technique could eliminate contributions from other complex baseline profiles in the quantitative analysis of spectral components.

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