Context: Infrared-faint radio sources (IFRS) are a class of radio-loud (RL) active galactic nuclei (AGN) at high redshifts (z 1:7) that are characterised by their relative infrared faintness, resulting in enormous radio-to-infrared flux density ratios of up to several thousand. Aims: Because of their optical and infrared faintness, it is very challenging to study IFRS at these wavelengths. However, IFRS are relatively bright in the radio regime with 1.4 GHz flux densities of a few to a few tens of mJy. Therefore, the radio regime is the most promising wavelength regime in which to constrain their nature. We aim to test the hypothesis that IFRS are young AGN, particularly GHz peaked-spectrum (GPS) and compact steep-spectrum (CSS) sources that have a low frequency turnover. Methods: We use the rich radio data set available for the Australia Telescope Large Area Survey fields, covering the frequency range between 150MHz and 34 GHz with up to 19 wavebands from different telescopes, and build radio spectral energy distributions (SEDs) for 34 IFRS. We then study the radio properties of this class of object with respect to turnover, spectral index, and behaviour towards higher frequencies. We also present the highest-frequency radio observations of an IFRS, observed with the Plateau de Bure Interferometer at 105 GHz, and model the multi-wavelength and radio-far-infrared SED of this source. ; Results: We find IFRS usually follow single power laws down to observed frequencies of around 150 MHz. Mostly, the radio SEDs are steep (α