In this article, we demonstrate the noise reduction and signal to noise ratio (SNR) enhancement in Brillouin optical time-domain analyzers (BOTDA). The results show that, although the main noise contribution comes from the Brillouin interaction itself, a simple low pass filtering on the detected radio frequency (RF) signal reduces remarkably the noise level of the BOTDA traces. The corresponding SNR enhancement depends on the employed cut-off frequency of the low pass filter. Due to the enhancement of the SNR, a mitigation of the standard deviation error of the Brillouin frequency shift (BFS) has been demonstrated. However, RF filters with low cut-off frequency could lead to distortions on the trace signals and therefore detection errors on a non-uniform BFS. The trade-off between the noise reduction and the signal distortion as well as an optimal cut-off frequency are discussed in detail.