Digital iterative deconvolution procedure (DIDP) and its smoothing properties to treat with experimental spectra

Abstract

A numerical procedure is proposed for finding a curve that provides a given curve (e.g., experimental spectral contour) in integral convolution with a known function. The experimental curve itself is assumed to be a zero approximation. In order to obtain the required function for the “ i” iteration, the “ i−1” iteration function is corrected by the difference between the experimental curve and the convolution of the “ i−1” iteration function. The solution obtained is not an oscillating function, as in Fourier self deconvolution, and allows (if necessary) for both the prohibition of a negative value and the limitation on the domain of the required function (break, cut-off). As an example, the statistical frequency distributions of the uncoupled vibrations of liquid water OH-oscillators have been calculated from the Raman spectra from 10 to 200°C. This procedure occurs also to be efficient for smoothing “noisy” experimental curves and involves only two parameters: the width of a “smoothing window” determining a resolution of the required details of the curve and the number of iterations.