A number of beam position monitors (BPM) are being installed at the Front End Test Stand (FETS) H– ion source at the Rutherford Appleton Laboratory, UK, as part of the 3 MeV medium energy beam transport. The FETS ion source delivers pulses up to 2 ms long at a rate up to 50 Hz and a maximum current of 60 mA, with a 324 MHz micro-bunch structure imposed by the frequency of the FETS RF acceleration cavity. The response of an in- house designed button BPM has been simulated and then characterised on a wire-based test-rig and the results are presented. The output from a custom algorithm running on a commercial PXI-based FPGA signal processing system is evaluated using test signals from both a function generator and the BPM in the test-rig, to verify the speed and precision of the processing algorithm. The processing system can determine the beam position in eight BPMs, with a precision of better than 20 μm, within one microsecond of the signal sampling being completed.