Moving differential and dynamic window moving averaging are simple and well-known signal processing algorithms. However, the most common methods of obtaining sufficient signal-to-noise ratios in distributed acoustic sensing use expensive and precise equipment such as laser sources, photoreceivers, etc., and neural network postprocessing, which results in an unacceptable price of an acoustic monitoring system for potential customers. This paper presents the distributed fiber-optic acoustic sensors data processing and noise suppression techniques applied both to raw data (spatial and temporal amplitude distributions) and to spectra obtained after the Fourier transform. The performance of algorithms’ individual parts in processing distributed acoustic sensor’s data obtained in laboratory conditions for an optical fiber subjected to various dynamic impact events is studied. A comparative analysis of these parts’ efficiency was carried out, and for each type of impact event, the most beneficial combinations were identified. The feasibility of existing noise reduction techniques performance improvement is proposed and tested. Presented algorithms are undemanding for computation resources and provide the signal-to-noise ratio enhancement of up to 13.1 dB. Thus, they can be useful in areas requiring the distributed acoustic monitoring systems’ cost reduction as maintaining acceptable performance while allowing the use of cheaper hardware.