MWA tied-array processing III: Microsecond time resolution via a polyphase synthesis filter

A new high time resolution observing mode for the Murchison Widefield Array (MWA) is described, enabling full polarimetric observations with up to 30.72 MHz of bandwidth and a time resolution of ~0.8 $\mu$s. This mode makes use of a polyphase synthesis filter to "undo" the polyphase analysis filter stage of the standard MWA's Voltage Capture System (VCS) observing mode. Sources of potential error in the reconstruction of the high time resolution data are identified and quantified, with the S/N loss induced by the back-to-back system not exceeding -0.65 dB for typical noise-dominated samples. The system is further verified by observing three pulsars with known structure on microsecond timescales.