  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. 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. We use the
rich radio data set available for the Australia Telescope Large Area Survey
fields, covering the frequency range between 150 MHz 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. We find IFRS
usually follow single power laws down to observed frequencies of around 150
MHz. Mostly, the radio SEDs are steep, but we also find ultra-steep SEDs. In
particular, IFRS show statistically significantly steeper radio SEDs than the
broader RL AGN population. Our analysis reveals that the fractions of GPS and
CSS sources in the population of IFRS are consistent with the fractions in the
broader RL AGN population. We find that at least 18% of IFRS contain young AGN,
although the fraction might be significantly higher as suggested by the steep
SEDs and the compact morphology of IFRS. The detailed multi-wavelength SED
modelling of one IFRS shows that it is different from ordinary AGN, although it
is consistent with a composite starburst-AGN model with a star formation rate
of 170 solar masses per year.
