Regularized Method of Spectral Curve Deconvolution

Abstract

A regularized method of spectral curve deconvolution is proposed. This method is based on three fundamental principles: the regularized method of solving the convolution equation; the use, instead of the apodization function, of the digital low-pass filter, which permits exact knowledge of its characteristics; and the use of the Fourier transform modulus of the spectrum being treated for obtaining a priori information about the frequency characteristics of the solution and noise, required for determination of the optimum parameters of the regularizing operator. The regularized method of de-convolution permits the acquisition of an approximately stable solution for the deconvolution problem of spectral curves, which moves toward an exact solution with the decrease of the experimental spectrum error. Examples are given of the application of the regularized method of deconvolution to simulated and experimental IR spectra. A conclusion about the expediency of using the given method for resolution enhancement in complex spectra is made.