## 3 Results  
As a part of the DAS optimization problem, it was decided to study the described algorithms operation in parts, in whole and together with various types of events recorded by the proposed design sensor (Figure 1). The sensing element consisted of 1 km of SMF-28 optical fiber. Four types of data were used for processing: 1 distributed event with a 2 kHz frequency, 1 distributed event with a 6.5 kHz frequency, 1 pointwise event with a 3 kHz frequency and harmonics at frequencies of 6 and 9 kHz, and one pointwise event with a 10 kHz frequency (Figure 5). Each data set contained both general background noise and signals that stood out against it and were not related to the useful one and did not depend on it (vertical bands corresponding to a certain frequency and recorded throughout the sensitive element, Figure 5). The frequency range taken into consideration was spaced between 0 and 11 kHz. The study of the noise reduction technique's effectiveness was carried out with those heat maps cross-sections (points of the optical fiber), in which the event had the highest amplitude, and in the case of a distributed event, with a frequency spectrum previously averaged over several points of the optical fiber. For each type of data, the algorithms of averaging over 20 neighboring elements in the spatial domain (SA--spatial averaging) and the moving differential (MD) in the time domain were first applied separately, and then together (filtering--F). After that, each of the four obtained results (NF--no filtering, SA, MD, and F) was subjected to the FFT, normalized to 1, and presented as input to the averaging algorithm with a dynamic window in the spectral domain (FDDA--frequency domain averaging). Figure 4: OFDR-trace before (**a**) and after (**b**) processing. IOM—integrated optical modulator. For data with a distributed event at a frequency of 2 kHz, the combination of SA and FDDA algorithms demonstrated the most significant increase in SNR by 1.6 dB (Figure 6c). Moreover, it was the SA algorithm that made it possible to eliminate noise peaks in the signal (Figure 6b). Presumably, this is due to the fact that they have a rather unstable amplitude in the spatial domain. The negative effects of the SA, MD algorithms, and their combination (F) resulting in an unsufficient increase or decrease of SNR are described in Section 4. However, it can be seen, that the FDDA algorithm, in its turn, not only exhibits edge effects--the noise level in the spectrum gradually increases from the edges to the middle but also places it above the zero level, whereas the spectrum does not contain components with an amplitude of less than a certain value, but greater than zero. These effects are explained by the fact that at the scanning dynamic window position \(i=0\), the first window element position in the array of discrete samples is equal to \(-w/2\), and at \(i=N\), the last window element falls to the position of \(N+w/2\). It is easy to determine that these positions do not exist in the array of discrete samples, so they were initially replaced by zeros. The larger the window on the array boundaries, the more impact zero-padded areas introduce. All this leads to the fact that the resulting data is allocated on a kind of \"pedestal\". Since the frequencies forming this pedestal are not physically present in the spectrum, they can be determined as noise and can be eliminated. The FDDA noise elimination algorithm modification can be represented as follows: first, a one-dimensional array M of input data with dimensions [0, (3\(N\)\(-\)1)] is created. It is filled according to  
\[M_{i}=P_{i-N\times floor(L(M)/N)} \tag{3}\]  
Figure 5: DAS data sets used for noise reduction techniques testing. (**a**) 2 kHz distributed event; (**b**) 6.5 kHz distributed event; (**c**) 3 kHz pointwise event with overtones frequencies of 6 and 9 kHz; (**d**) 10 kHz pointwise event. The setup used is shown in Figure 1.  
Figure 6: The steps of 2 kHz event (Figure 5a) data processing.