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.