## 6 Conclusions  
Due to the presence of noise, the interpretation of various measurements requires the use of signal processing algorithms. Also, for measurements of FBG sensor spectra, various algorithms have been developed to estimate the Bragg wavelength and its shift. This article presents methods that reduce the noise in the measurement data for demodulation of the Bragg wave shift. The first group of methods includes nonlinear filtration, while the second is the operation of raising the spectrum value to the second power. Algorithms based on geometric filtration and its modifications reproduce the Gaussian shape well. A weaker level of noise elimination can be observed for small intensity values. A method of reducing this phenomenon, which is proposed in this article, is adding a specific offset value to the spectrum before applying the filter and subtracting this value after the filtration operation. The second method is using combined arithmetic and geometric filtration operations. This nonlinear filter has better properties than a geometric filter. With simulation data, it was found that raising the spectrum to the second power reduced the RMSE value of the shift determination for the entire considered SNR range. Before raising the spectrum to the power, it is beneficial to perform cross-correlation or, equivalently, smoothing filtration. However, unlike in the case of typical spectrum analysis, the basic condition is not preserving the peak intensity but significantly blurring it. Thanks to this, the signal-to-noise ratio in the spectrum significantly increases after filtration and raising to the second power. The analysis of the experimental spectra revealed the influence of the climatic chamber operation on the vibrations, which were noticeable in the measurements, especially in the phase of changing the temperature settings. Measurements with the temperature stabilisation function switched off significantly reduced the fluctuations of the determined wavelength compared to stabilisation during operation. The beneficial influence of the use of nonlinear  
Figure 20: Comparison of the spectra of the gratings used in the measurements.  
\begin{table}
\begin{tabular}{c c c} \hline
**Algorithm** & \(\delta\lambda\)**=0.004 nm** & \(\delta\lambda\)**=0.02 nm** \\ \hline Centroid & 0.0506 & 0.501 \\ \hline Power of spectrum–centroid & 0.0405 & 0.412 \\ \hline FPC & 0.0401 & 0.410 \\ \hline Power of spectrum–FPC & 0.0407 & 0.409 \\ \hline Nonlinear filter (\(k\) = 40)–FPC & 0.0409 & 0.410 \\ \hline Cross-correlation–FPC & 0.0407 & 0.082 \\ \hline Cross-correlation–square–FPC & 0.0405 & 0.081 \\ \hline \end{tabular}
\end{table}
Table 3: Comparison of RMSE for individual algorithms and two spectral resolutions, \(\delta\lambda\) = 0.004 nm and \(\delta\lambda\) = 0.02 nm.  
filtration and raising the spectrum to the second power was also demonstrated in the case of experimental measurements.  
[PERSON] contributed to the idea of this work. [PERSON], [PERSON], [PERSON] and [PERSON] performed data analysis, [PERSON] and [PERSON] performed the experiments. This article was written by [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Lublin University of Technology (grant number: FD-20/EE-2/301).  
Not applicable.  
Data Availability Statement: Data are contained within this article.  
The authors declare no conflicts of interest.