In recent years, the Brigham Young University (BYU) Radio Astronomy Systems group has developed phased-array feeds and the data acquisition processing systems necessary to perform radio astronomy observations. This thesis describes the development and testing of a real-time digital beamforming system that reduces both the time required to process phased-array feed data and the disk space used to record this data compared to post-processing beamforming systems. A real-data experiment is also discussed in this thesis, which focuses on some of the data post-processing required for one of BYU's data acquisition systems.Radio-frequency interference mitigation techniques for phased-array feed radio astronomy have been studied for several years, but the effect that these techniques have on weak-signal detection is not well understood. This thesis provides analysis of a simulated weak-source observation for the Green Bank 20-meter telescope and BYU 19 element phasedarray feed with radio-frequency interference present. Interference mitigation techniques are shown to reduce the detectability of weak sources compared with the no interference case, but it is also shown that a weak source can be detected that would otherwise be masked by interference.