An optically preamplified digital pulse position modulation (PPM) receiver with an improved electrical domain filtering regime, involving a matched filter in cascade with a pulse shaping network, is rigorously analysed for the first time. Sensitivity results for various length PPM words, bit error rate curves, and an examination of the pulse shaping network behaviour are presented. In comparison to an equivalent on-off keyed non-return to zero (OOK NRZ) system the results show a possible benefit of 8.1 dB and in fact surpass the fundamental sensitivity limit of such a receiver, approaching the sensitivity of coherent detection. In particular the analysis suggests that at the STM-4 bit-rate of 622 Mbit/s a sensitivity of 21.54 photons/bit is attainable. Removing the pulse shaping network incurs a penalty of 1.9 dB for high PPM coding levels, though it is lower at the optimum coding level. The optical fibre PPM power spectral density is derived in a simple fashion and the effect of timing jitter on this detection regime is considered for the first time, showing a sensitivity penalty of less than 0.9 dB for the parameters considered.