The radio-wavelength detection of extensive air showers (EAS) initiated by cosmic-ray interactions in the Earths 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 MWAs 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.
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