Modification of Derivatives for Resolution Enhancement of Bands in Overlapped Spectra

Abstract

A method for obtaining modified derivatives based on the multiplication of the Fourier image of a normal derivative of degree n by the function (– iSign( x)) n has been considered. The thus-obtained modified derivatives of even, odd, and fractional degrees of symmetric functions are also even functions, which permits one to use them for obtaining spectra with a better resolution of individual bands. Also, the use of derivatives of various degrees makes it possible to considerably widen the set of functions suitable for resolving individual bands in overlapped spectra. The results of the application of modified derivatives to synthetic and experimental spectra have been considered. The conclusion has been drawn that practical application of such derivatives permits more flexible variation of the resolution in the resulting spectrum compared to the normal derivatives of only even orders.