A series of beam position monitors (BPMs) will be installed at the Front End Test Stand (FETS) at RAL as part of the 3 MeV Medium Energy Beam Transport (MEBT). The BPMs analyse 2 ms long, 60 mA beam pulses delivered to the MEBT by a 324 MHz Radio Frequency Quadrupole (RFQ). Initial linearity and resolution measurements from the prototype button BPMs are shown. The development of the algorithm for the processing of the BPM signals using a commercial PXI-based FPGA card is discussed and initial measurements of the electronics and signal processing are presented. The test-rig used to characterise each BPM and further develop the processing algorithm is described. The position and phase are measured several times throughout the duration of each pulse, and the measurements are made available via an EPICS server.