  The radio-wavelength detection of extensive air showers (EAS) initiated by
cosmic-ray interactions in the Earth's atmosphere is a promising technique for
investigating the origin of these particles and the physics of their
interactions. The Low Frequency Array (LOFAR) and the Owens Valley Long
Wavelength Array (OVRO-LWA) have both demonstrated that the dense cores of low
frequency radio telescope arrays yield detailed information on the radiation
ground pattern, which can be used to reconstruct key EAS properties and infer
the primary cosmic-ray composition. Here, we demonstrate a new observation mode
of the Murchison Widefield Array (MWA), tailored to the observation of the
sub-microsecond coherent bursts of radiation produced by EAS. We first show how
an aggregate 30.72 MHz bandwidth (3072x 10 kHz frequency channels) recorded at
0.1 ms resolution with the MWA's voltage capture system (VCS) can be
synthesised back to the full bandwidth Nyquist resolution of 16.3 ns. This
process, which involves `inverting' two sets of polyphase filterbanks, retains
90.5% of the signal-to-noise of a cosmic ray signal. We then demonstrate the
timing and positional accuracy of this mode by resolving the location of a
calibrator pulse to within 5 m. Finally, preliminary observations show that the
rate of nanosecond radio-frequency interference (RFI) events is 0.1 Hz, much
lower than that found at the sites of other radio telescopes that study cosmic
rays. We conclude that the identification of cosmic rays at the MWA, and hence
with the low-frequency component of the Square Kilometre Array, is feasible
with minimal loss of efficiency due to RFI.
