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A conventional method to denoise signals in Brillouin optical time-domain analysis (BOTDA) sensors is ensemble averaging. This method necessitates the acquisition of thousands of signals to provide an acceptable signal-to-noise ratio (SNR). The signal acquisition is a time-consuming process that drastically increases the measurement time of BOTDA sensors. This paper presents a novel method on the basis of the adaptive linear prediction (ALP) technique to reduce the measurement time of such sensors. The conventional setup of BOTDA sensors is modified to denoise signals using the ALP technique before applying ensemble averaging. The application of the ALP technique removes a significant portion of noise while it preserves the abrupt changes and smooth pieces of signals. As a result, the number of signals required to obtain accurate measurements and, consequently, the measurement time of the sensor are reduced by up to 90%. This modification enables BODTA sensors to implement dynamic measurements of temperature and strain and opens opportunities to address a new range of applications.