  Broadband precision spectroscopy is indispensable for providing high fidelity
molecular parameters for spectroscopic databases. We have recently shown that
mechanical Fourier transform spectrometers based on optical frequency combs can
measure broadband high-resolution molecular spectra undistorted by the
instrumental line shape (ILS) and with a highly precise frequency scale
provided by the comb. The accurate measurement of the power of the comb modes
interacting with the molecular sample was achieved by acquiring single-burst
interferograms with nominal resolution precisely matched to the comb mode
spacing. Here we give a full theoretical description of this sub-nominal
resolution method and describe in detail the experimental and numerical steps
needed to retrieve ILS-free molecular spectra, i.e. with ILS-induced distortion
below the noise level. We investigate the accuracy of the transition line
centers retrieved by fitting to the absorption lines measured using this
method. We verify the performance by measuring an ILS-free cavity-enhanced
low-pressure spectrum of the 3{\nu}1+{\nu}3 band of CO2. We observe and
quantify collisional narrowing of absorption line shape, for the first time
with a comb-based spectroscopic technique. Thus retrieval of line shape
parameters with accuracy not limited by the Voigt profile is now possible for
entire absorption bands acquired simultaneously.
