An interpolation formula is derived which gives an apodized spectrum as the convolution of the unapodized spectrum (sampled at suitable points) with the apodized apparatus function. This allows many apodizations to be applied to a single interferogram with the performance of only a single Fourier transformation. A further saving in computation effort is possible if the apodized apparatus function decays rapidly away from its center. Examples of such cases are presented, where the interferogram is weighted by a function which is a cosine series of only a few terms.
A. S. FILLER, "Apodization and Interpolation in Fourier-Transform Spectroscopy," J. Opt. Soc. Am. 54, 762-764 (1964)