Phase-matched filters are defined as a class of linear filters in which the Fourier phase of the filter is made equal to that of a given signal. An iterative technique is described which can be used to find a phase-matched filter for a particular seismic signal. The process is then applied to digital records of Rayleigh waves from a synthetic source with propagation across 55° of continental path, an earthquake in the Greenland Sea recorded in Texas, and a nuclear explosion in Novaya Zemlya recorded in New Mexico. Application of the filter allows multiple arrivals to be identified and removed and allows recovery of the complex spectrum of the primary wave train along with its apparent group-velocity dispersion curve. The amplitude spectrum of the primary signal obtained by this linear process is not contaminated by interference from multipath arrivals. The filtering process also provides significant improvement in signal-to-noise ratio, greater than a factor of four for the Greenland Sea and Novaya Zemlya events.