ABSTRACT
Modern spectrometers are mostly controlled by microprocessors, and on-line connections with computers enable the acquisition of spectral data while recording on external storage media. The fact that the whole continuous function is not used for numerical processing, but only the part represented by the digitized points influences the amount and quality of information obtained from the digitized spectrum. This chapter focuses on the methods of numerical differentiation, which can be divided into two main groups. The procedures used for direct differentiation, i.e., obtaining the values of derivatives directly from experimental data using the differences, form the first group. The methods of curve fitting, i.e., approximating the spectral data by segments of analytical functions and derivatives obtained analytically by differentiation of the corresponding functional relationships, belong to the second group. In principle, all procedures yielding derivatives tabulated from the functional values detailed in various handbooks of numerical mathematics are direct differentiation methods.
