Fractional derivative for finding width, amplitude and shape of overlapping peaks

Abstract

This work describes a technique based on fractional derivative for finding the overlapping peaks spectral parameters. This is due to positive effects of the fractional derivative caused by the behavior of its zero-crossing and maximal amplitude. A power of the method is demonstrated for synthetic data by using the well-known distributions such as Lorentzian, Gaussian ones and for experimental infra-red spectra coming from molecular spectroscopy. It is shown that recorded spectra are approximated with the Tsallis distribution in the best way, compared to the distributions above mentioned.