Reliable weather parameter estimates are required of radars such as the Terminal Doppler Weather Radar (TDWR) - a Federal Aviation Administration project - which will automatically detect hazaradous weather phenomena in the vicinity of an airport. Velocity and range aliasing will degrade the quality of these estimates, as will contamination by ground clutter. For radars which operate at short ranges and at low elevation angles, as the TDWR will to detect windshears at the airport surface, clutter contamination is an especiallly severe problem. Multirate pulse trains - pulse trains containing multiple intersample spacings - can extend both the unambiguous velocity and range of a Pulsed Doppler Radar beyond those afforded by pulse trains with a constant intersample spacing; but the usual properties of conventional clutter filter architectures change radically when applied to data collected with a multirate sampling scheme. A brief introduction to the systems and weather considerations fo Doppler Weather Radars is provided and the Pulse-Pair spectral moment estimators are presented. This introduction is followed by a discussion of frequency domain clutter rejection tecniques for Batch PRT (Pulse Repetition Time) sequences - blocks of equispaced samples with the PRT alternating from block to block. The main topic of the report is clutter suppression for Staggered PRT sequences in which the PRT alternates from pulse to pulse. The Staggered PRT scheme has the advantage over the Batch PRT scheme of spatial coherency for estimates of the radar return signal's autocorrelation function at the lags corresponding to the two PRT's. A time-varying filter architecture with multiple transfer functions is presented and analyzed, and its interaction with the Pulse-Pair estimators is explored. Three design techniques for Staggered PRT filters are described and assessed in the context of clutter suppression. The final section of the report summarizes the results for the Batch and Staggered PRT schemes and provides suggestions for further research.