Pretreating near infrared spectra with fractional order Savitzky–Golay differentiation(FOSGD)

With the aid of Riemann–Liouville fractional calculus theory,fractional order Savitzky–Golay differentiation（FOSGD） is calculated and applied to pretreat near infrared（NIR） spectra in order to improve the performance of multivariate calibrations.Similar to integral order Savitzky–Golay differentiation（IOSGD）,FOSGD is obtained by fitting a spectral curve in a moving window with a polynomial function to estimate its coefficients and then carrying out the weighted average of the spectral curve in the window with the coefficients.Three NIR datasets including diesel,wheat and corn datasets were utilized to test this method.The results showed that FOSGD,which is easy to compute,is a general method to obtain Savitzky–Golay smoothing,fractional order and integral order differentiations.Fractional order differentiation computation to the NIR spectra often improves the performance of the PLS model with smaller RMSECV and RMSEP than integral order ones,especially for physical properties of interest,such as density,cetane number and hardness.