A general computational method for converting normal spectra into derivative spectra

Y.L. Yeow, Yee-Kwong Leong

Research output: Contribution to journalArticle

9 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)584-592
JournalApplied Spectroscopy
Issue number5
Publication statusPublished - 2005


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