We report a rotationally resolved analysis of the high resolution FTIR spectrum of naphthalene which can be considered as a prototypical molecule for polycyclic aromatic hydrocarbons (PAHs), and a similar analysis for the prototypical heterocyclic aromatic molecule indole. The spectra have been measured using a resolution of 0.0008 cm^-1 (21 MHz) with the new high resolution FTIR prototype spectrometer of the Molecular Kinetics and Spectroscopy Group at ETH Zürich. The spectrometer is connected to the infrared port available at the Swiss Light Source (SLS) at the Paul-Scherrer-Institute (PSI). Due to the high brightness of the synchrotron radiation in the spectral region of interest, effectively up to 20 times brighter than thermal sources, and the high resolution of the new interferometer, it was possible to record the rotationally resolved infrared spectra of naphthalene and indole at room temperature, and to analyse the ν₄₆ c-type band (ṽ₀ = 782.330949 cm^-1) of naphthalene as well as the ν₃₅ c-type band (ṽ₀ = 738.483592 cm^-1) of indole and an a-type band at ṽ₀ = 790.864370 cm^-1 tentatively assigned as the overtone 2ν₄₀ of indole. The results of the naphthalene band analysis are discussed in relation to the Unidentified Infrared Band (UIB) found in interstellar spectra at 12.8 μm.