The general theory of Fourier self-deconvolution, i.e., spectral deconvolution using Fourier transforms and the intrinsic lineshape, is developed. The method provides a way of computationally resolving overlapped lines that can not be instrumentally resolved due to their intrinsic linewidth. Examples of the application of the technique to synthetic and experimental infrared spectra are presented, and potential applications are discussed. It is shown that lines in spectra having moderate signal/noise ratios (∼1000) can readily be reduced in width by a factor of 3. The method is applicable to a variety of spectroscopic techniques.

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Algorithms for the computation of bandwidths, and center of gravity and least-squares frequencies are developed. The sources of error are discussed, and it is shown that the above parameters can be determined with maximum uncertainties of hundredths or thousandths of a wave number.

A general formula for computing changes in the signal-to-noise ratio of a spectrum resulting from the Fourier self-deconvolution procedure is derived. Self-deconvolution reduces the intrinsic halfwidths of lines by a factor K, which is in practice limited by the noise in the spectrum. With the help of the derived formula, the rate of decrease in the SNR as a function of K for eight different smoothing (apodization) functions is studied. With high K values there are significant differences in the SNR as a result of the use of different smoothing functions. With K = 4 a difference of more than 1 order of magnitude between two extreme cases is demonstrated, and with K = 5 a difference of almost 2 orders of magnitude in the SNR is predicted.

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