A numerical procedure for curve fitting of noisy infrared spectra

A method for the detection of overfitting of noisy spectra is presented. Wh en 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 t oward more negative values, while the Wald-Wolfowitz test tends to give mor e positive values, as the data is overfitted. Models that give residuals wi th a non-random ordering may be rejected. The use of these functions for th e determination of the "best" fitting of several approximations (Savitzky-G olay smoothing, segmented osculating polynomials (SOPA), Fourier series, an d Lorentzian bands) to a noisy synthetic spectrum, and the application to i nfrared spectra of coal, is shown. (C) 1998 Elsevier Science B.V. All right s reserved.