## 3 Results
(**a**) Original spectrum; (**b**) spectrum obtained after SA algorithm filtering; (**c**) spectrum resulting from SA and subsequent FDDA algorithms filtering. where _floor_(_x_) returns an integer part of \(x\), _L_(_x_)--returns \(x\) length. Thus, the values of the array \(M\) will correspond to the following original signal values _P_:  
\[ \begin{array}{l}M_{i}=P_{i},\;i\in[0,(N-1)];\\ M_{i}=P_{i-N},\;i\in[(N-1),(2N-1)];\\ M_{i}=P_{i-2N},\;i\in[(2N-1),(3N-1)].\end{array}  \tag{4}\]  
Next, the resulting array \(M\) is processed according to Equation (2), and its values are replaced with the new ones. The received data is used to form a new _M_\({}^{\prime}\) array of [0, (_N_\(-\)1)] size:  
\[ \begin{array}{l}M_{i}^{\prime}=M_{i+N}\end{array}  \tag{5}\]  
After that, the sample m representing the minimum value is found in the array _M_\({}^{\prime}\), by iterative enumeration. _M_\({}^{\prime}\) values are overwritten as follows:  
\[ \begin{array}{l}M_{i}^{\prime}=M_{I-m}^{\prime}\end{array}  \tag{6}\]  
Then the values of _M_\({}^{\prime}\)_ are normalized to 1. Thus, the elimination of the noise pedestal in the processed spectrum is achieved. The FDDA modification made it possible to reach an increase in SNR in the studied case by 9.7 dB (Figure 7a). Therefore, for an distributed event with a 2 kHz frequency, the SNR turned out to be 20.6 dB after processing. In the initial data, it was equal to 10.9 dB. The results of distributed 6.5 kHz frequency event processing were practically the same (Figure 7b)--the considered combination of algorithms provided an increase in SNR by 13.1 dB. For a frequency spectrum of a 3 kHz pointwise event with harmonics, the SNR was 14.7 dB  
was not taken into consideration, a significant increase in the noise level did not affect the SNR. However, in the case of the 3 kHz event frequency, this effect began to provide a significant contribution, affecting not only the SNR but also distorting the intensity values in the useful signal. This resulted in the harmonics with frequencies of 9 and 3 kHz getting an amplitude greater than that of the fundamental tone (Figure 8d). Describing the case of 10 kHz event, it should be noted that the SA algorithm processing had a negative impact here, since it led to the rise of spurious peaks associated with noise that were almost imperceptible in the original spectrum (Figure 8a). The FDDA algorithm, which proved to be quite effective in all the cases studied, nevertheless, has at least one drawback. If the useful signal components are located close enough in the frequency domain, the noise components between them will be reduced less compared to the area near the single-frequency event. The modified algorithm significantly reduces the effect, but does not eliminate the problem entirely (Figure 9b). This is due to the peculiarities of this algorithm operation and, in particular, the mechanism for the selection of window size, as the latter depends on the presence of the significant signal level increases nearby. In the case of the 3 kHz event, this manifested itself in the form of a spectrum noise component convex shape, which slightly decreased the SNR relative to the expected value (Figure 9c). Figure 8: A demonstration of considered noise filtering techniques disadvantages. Spectrum of (**a**) 10 kHz event before processing; (**b**) 10 kHz event resulting from SA algorithm processing; (**c**) 3 kHz event before processing; (**d**) 3 kHz event resulting from MD algorithm processing. As already noted, the presented methods have both advantages and disadvantages. In general, when using both algorithms, part of the useful signal may be missed. It can be either a high-frequency signal or a signal of any frequency, but with a relatively low amplitude. To eliminate this shortcoming in the future, it is advisable to use the methods of machine learning and artificial intelligence [55; 56; 57], which can be used in combination with the described approaches.