Effect of the degree of polynomials in the Savitzky—Golay method for calculation of second-derivative spectra

The second-derivative spectra of absorption curves simulated by a Gaussian function were obtained by using Savitzky—Golay cubic (CPC) and quintic polynomial convolutions (QPC), based on 17 points assumed to be at 0.25-nm intervals. For data obtained directly from the simulated curves (real-type data), the second derivatives agreed with the true values if the widths at half height of the peaks were > 15 nm for CPC and 5 nm for QPC. But when integer values obtained from the real-type data were used to simulate a 12-bit A/D conversion, considerable noise appeared on the second-derivative spectra of peaks wider than the above values, obtained by both CPC and QPC. This occurred because the rounding errors introduced by the A/D conversion formed small shoulders on the digitally reproduced absorption curves, which were enhanced by the differentiation to generate noise. The noise was more intense in QPC than in CPC, thus CPC is preferable for peaks that are not very narrow.