Modern airport surveillance radars (ASR) are coherent pulsed-Doppler radars used for detecting and tracking aircraft in terminal area air-space. These radars might serve an additional role by making radial wind measurements in the immediate vicinity of an airport to provide data on low altitude wind shear (LAWS). One factor that will affect their capability in this role is the requirement that intense low-beam ground clutter be filtered from the signals prior to estimation of the reflectivity and radial velocity of weather scatterers. This report describes and analyzes a specific signal processing algorithm for ASR weather parameter measurements. An adaptively selected Finite Impulse Repsonse high-pass filter is used for ground clutter suppression, followed by pulse-pair weather reflectivity and radial velocity estimation. Measurements from a Lincoln Laboratory-developed testbed ASR in Huntsville, Alabama are used to characterize the ground clutter environment under siting ocnditions that are representative of operational ASRs. Temporal fluctuations in ground clutter intensity are analyzed with attention to their impact on the adaptive clutter-filter selection procedure. The performance of the signal processing algorithms is then analyzed using the testbed ASR ground clutter measurements in combination with simulated or real weather signals. We conclude that ground clutter and hte requisite clutter filtering will not severely distort ASR wind shear measurements when the reflectivity factor of the microburst or gust front is approximately 20 dBz or greater. This is typically the case for microbursts ocurring in moist conditions such as prevail over the Eastern United States during summer.