  Fourier transform spectroscopy based on incoherent light sources is a
well-established tool in research fields from molecular spectroscopy and
atmospheric monitoring to material science and biophysics. It provides
broadband molecular spectra and information about the molecular structure and
composition of absorptive media. However, the spectral resolution is
fundamentally limited by the maximum delay range ({\Delta}$_{max}$) of the
interferometer, so acquisition of high-resolution spectra implies long
measurement times and large instrument size. We overcome this limit by
combining the Fourier transform spectrometer with an optical frequency comb and
measuring the intensities of individual comb lines by precisely matching the
{\Delta}$_{max}$ to the comb line spacing. This allows measurements of
absorption lines narrower than the nominal (optical path-limited) resolution
without ringing effects from the instrumental lineshape and reduces the
acquisition time and interferometer length by orders of magnitude.
