A general computational method for converting normal spectra into derivative spectra

The mathematical problem of converting a normal spectrum into the corresponding first- and second-derivative spectra is formulated as an integral equation of the first kind. Tikhonov regularization is then applied to solve the spectral conversion problem. The end result is a set of linear algebraic equations that takes in as input the original spectrum and produces as output the second-derivative spectrum, which is then integrated to yield the first-derivative spectrum. Noise amplification is kept under control by adjusting the regularization parameter (guided by generalized cross-validation) in the algebraic equations. The performance of this procedure is demonstrated by applying it to different types of spectral data taken from the literature.