Using the Tsallis distribution and the fractional differentiation to resolve the overlapping bands

Using the Tsallis distribution, which facilitates the generalization of well-known distributions such as Gaussian and Lorentzian by varying a non-extensivity parameter q as a model of the individual band to correctly assign overlapping bands and the fractional differentiation as mathematical tool to help to determine the spectral parameters of the individual band, a new resolution method for the overlapping bands is presented. According to variation of the maximum and the zero-crossing of the Tsallis distribution at different differential order, two types of parameter estimators are obtained, which are utilized to calculate the parameters of position, height, and width of Tsallis distribution. To verify the suggested method, separation of several kinds of overlapping bands simulated by computer and the experimental infrared spectrum of 1,2-bromofluoroethane have been performed and discussed. Figure α-Order differentiation of the overlapping band