With the increased penetration of phasor measurement units (PMUs) within the power grid, there is a clear need for understanding the different filtering techniques which can be used to convert raw measurements into usable data. Because of the high sampling rate of PMUs, there are relatively high frequency components present in PMU signals when compared to traditional power system measurements. These components, which can range from 0.1 Hz to half the PMU sampling frequency, must be filtered out before the data can be used with steady state analysis techniques. This paper compares the performance of two different means of filtering out this higher frequency data - FIR filtering and median filtering. Several metrics are defined to quantify the behavior of these filters with a particular emphasis on handling measurements before and after system events. Results are presented based on both real and simulated PMU data. Based on these tests, observations regarding the advantages and disadvantages of the two filter types are discussed.