We present a new system for high repetition rate and real-time pulse analysis implemented at the Monoenergetic Positron Source (MePS) at the superconducting electron LINAC ELBE at Helmholtz-Zentrum Dresden-Rossendorf. Dedicated digital signal processing and optimized algorithms are employed allowing for high bandwidth throughput, online pulse analysis and filtering. Positrons generated from radioisotopes and from bremsstrahlung pair production by means of highly intense accelerator-based positron beams serve as a microstructure probe allowing material characterizations with respect to chemical, mechanical, electrical, and magnetic properties. Positron annihilation lifetime events with up to 13 MHz repetition rate are being processed online without losses while performing signal selections for pile-up reduction, online energy calibration, and — for radioisotope-based measurements — identification of start and stop events.