An operation common to many applications of high-speed, real-time signal processing is two-dimensional filtering. Recent advances in memory technblogy and residue arithmetic allow high-speed implementation. A two-dimensional five-by-five matrix convolution filter for pulse matching was implemented in residue arithmetic using programmable read only memory (PROM). The simple architecture of this all-PROM filter permits easy pipeline design and the inherent modular structure of residue arithmetic minimized the design overhead. The filter operates at 20 million operations per second with emitter coupled logic (ECL) PROMs. This filter has options such as elementary error detection, multiple patterns matching, and adaptive filtering. An Intel 8086 microprocessor was used as a controller to the filter.