Power system monitoring is the basis of realizing operation safety and stability. The increasing integration of renewable energy generation along with the growing diffusion of nonlinear loads and micro-generators complicates the characteristics of low voltage grid, which leads to new requirements for the synchronized dynamic monitoring in low voltage electrical network. Unfortunately, the signal waveform in low voltage grid is polluted by heavy noises, which will influence the estimation accuracy of synchronized frequency measurement at low voltage side. Firstly, this paper summarizes the noise characteristics of synchronized frequency measurement at low voltage side, including white gaussian noise, random impulsive noise and periodic impulsive noise. Secondly, based on the noise characteristic, median filtering and mean filtering methods are analyzed as the best choice of the fast noise filter. Thirdly, the optimal parameter of the filter is analyzed by simulation. The optimal length of filter window can be determined according to this simulation result in the condition that SNR is known. Finally, one filtering case of the frequency signal recorded by PMU Light is analyzed, which proves that the noise can be filtered effectively by the filter. It is worthy to emphasize that this fast filtering method is a good choice of measurement preprocessing for various online applications of synchronized frequency measurement in low voltage network.