This paper presents a technique for defining the optimal parameters of a moving window when processing the signal of a vibration accelerometer installed on a ball drum mill as part of the automation system. Time series signals of the vibration acceleration have been synthesized based on the experimental data of frequency spectrums with the application of the inverse Fourier transform. The lower and upper limits for the moving window size have been defined. The frequency spectrum for the time series signal within the moving window has been built by means of the fast Fourier transform method. An optimality criterion has been proposed. This criterion considers the quality of the derived frequency spectrum and the computational resources of the microprocessor system needed for processing the vibration accelerometer signal. The optimal duration of the moving window for the analyzed example is 100 ms. The impact of the time signal sampling rate on the frequency spectrum shape has been studied.