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(38) Polynomial fitting approach to fractional derivatives of NIR spectra

Jun Uozumi
Abstract Book of the 2nd Asian NIR Symposium (ANS2010), pp.17-18, 2010-10


Derivatives of the first and second orders are effective pretreatments in many cases in establishing NIR calibration. To expand the utility of these pretreatments by removing the limitation on the order, derivatives of arbitrary positive orders, or fractional derivatives (FDs), were introduced and were shown to give better estimation performance as compared with ordinary derivatives. In the case of FDs, reduction of noises growing with an increase in derivative order relied only on the low-pass filtering in Fourier space, which however also reduces the resolution of signals. In this paper, to improve this situation, an alternative approach based on polynomial fitting is proposed for calculating FDs. By this approach, noises are effectively reduced with fine structures of FDs retained.

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