A numerical procedure for curve fitting of noisy infrared spectra Original Research Article

A method for the detection of overfitting of noisy spectra is presented. When fitting data that contains random noise, the autocorrelation function (RL) of residuals at lag 1 (R1) 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.