Fourier transform spectrometers replace the traditional dispersive frequency analyzer by a Michelson interferometer. The spectrum is the Fourier transform of the interferogram constituting the raw output. The method is a primary tool for chemical analysis because it has decisive advantages over the dispersive one for analyzing infrared electromagnetic radiation (Fourier transform infrared, FTIR). A new procedure for dealing with the raw interferometric output of the instrument, not needing Fourier transformation and having additional advantages, is put forward here. It rests on recent advances in the theory of the interaction of matter with electromagnetic radiation yielding first principles analytic expressions for the Fourier transform of the spectral lineshapes, which can be fitted directly to the experimentally measured interferogram. The relevant physical information, as the integrated intensities of the electronic transitions and their net energy release, not affected by Stokes shifts, is readily obtained in the fitting procedure. Ulterior analysis of the spectra, introducing phenomenological standard interpolation functions to deconvolute and integrate peaks, becomes unnecessary. Both methods, standard FTIR and the one outlined here, demand little computer time and can be used simultaneously with synergistic effects.