Fourier Deconvolution in Non-Self-Deconvolving Conditions. Effective Narrowing, Signal-to-Noise Degradation, and Curve Fitting

Abstract

The effect of Fourier deconvolution on band narrowing and on the decrease of signal-to-noise ratio has been studied for a generalized case in which the width used in the deconvolution does not match the actual bandwidth. For the identification of underlying component bands, our results show that application of infra-deconvolution (i.e., the bandwidth used for deconvolution is lower than the actual bandwidth) produces a high degradation of the signal-to-noise ratio and poor band narrowing. On the contrary, self- or over-deconvolution, with lower signal-to-noise degradation and higher band narrowing, seem more suitable for this purpose. Relative to quantitative analysis, we rely on both theoretical and practical aspects to propose the generalized use of Voigt band shapes as a fairly correct general model to be used in the curve fitting of deconvoluted bands. With its use, the curve fitting of noise-free deconvoluted bands retrieved the original band parameters with high accuracy. The noise effect on the parameter precision obtained by curve fitting a deconvoluted noisy Lorentzian band was also studied. Finally, the existence of optimum deconvolution parameters for curve fitting complex spectra is considered, and a general recommendation for approaching this optimum is given.