期刊
APPLIED SPECTROSCOPY
卷 59, 期 5, 页码 584-592出版社
SOC APPLIED SPECTROSCOPY
DOI: 10.1366/0003702053946056
关键词
spectral conversion; derivative spectra; ill-posed problem; integral equation; Tikhonov regularization
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.
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