A numerical procedure for curve fitting of noisy infrared spectra

A method for the detection of overfitting of noisy spectra is presented. When fitting data that contains random noise, the autocorrelation function (R-L) of residuals at lag 1 (R-1) approaches zero and then shows a tendency toward more negative values, while the Wald-Wolfowitz test tends to give more positive values, as the data is overfitted. Models that give residuals with a non-random ordering may be rejected. The use of these functions for the determination of the "best" fitting of several approximations (Savitzky-Golay smoothing, segmented osculating polynomials (SOPA), Fourier series, and Lorentzian bands) to a noisy synthetic spectrum, and the application to infrared spectra of coal, is shown. (C) 1998 Elsevier Science B.V. All rights reserved.