## 1 Introduction  
The development of fibre optic periodic structures is accompanied by an ever-increasing number of associated applications. Improvements and modifications to measurement systems are aimed at enabling the accurate determination of the value of analysed quantities. A fundamental issue in the case of sensors is the appropriate analysis of measurement signals. In the case of optical sensors, we analyse optical signals, and for periodic structures, the analysed signals are optical spectra. In order to fully use the information contained in optical spectra, they must be subjected to the appropriate mathematical operations. New demodulation algorithms are being developed for most sensors requiring optical spectrum measurement. Fibre optic Bragg gratings have a wide range of interesting applications. Despite the relatively simple spectrum, most often in the form of a single Gaussian shape, there are a significant number of algorithms for demodulating such structures. The spectra of tilted fibre Bragg gratings are much more complex. Information about the physical quantities affecting TFBG is encoded in the optical spectrum. The basic element of the TFBG spectrum is a single cladding mode resonance, which repeats to form a cladding mode comb. More advanced methods are used to demodulate such a complex spectrum. Most often, as a result of the demodulation algorithm, a parameter representing the spectrum and correlated with the analysed quantity is determined. The first parameter established on the basis of changes in the TFBG spectrum was the area occupied by cladding modes [1]. Its basic use was to determine the refractive index. The envelope area can be combined with various quantities acting on the sensor, such as bending or immersion level. Further algorithms using quantitative spectrum parameters include spectrum length and advanced methods for calculating the area of cladding modes. The second approach to determining parameters based on TFBG spectra is to identify the cut-off wavelength, i.e., a parameter in the wavelength domain. The cut-off wavelength shift can be preceded by filtering in the Fourier transform domain [2]. The filters used to analyse TFBG spectra have rectangular shapes in the frequency domain [3]. The third group are methods that use parameters in the domain of appropriate transformations, such as the Fourier transform mentioned earlier, for the purpose of filtering. An example would be the centroid under the curve of the fundamental frequency band calculated using fast Fourier transform [4]. There are also methods that use local features of the spectrum, such as small local shifts of individual cladding modes with a constant amplitude value [5; 6]. Determining the value of the refractive index is used in many fields of science and technology. Refractometers can be used to determine the concentration of various substances such as paracetamol [7]. Finding the SRI (surrounding refractive index) value based on the TFBG optical spectrum requires establishing the appropriate spectrum parameter. Parameters that can be calculated in a simple and effective way are preferred. Unnecessary steps should be avoided, especially those that do not improve the quality of the results obtained. Frequency-selective, smoothing, and differentiation filters are commonly used in signal analysis. Differential filtering requires appropriate selection of the method due to the amplification of higher frequencies, which may result in the amplification of noise contained in the data. The selection of appropriate algorithms requires an in-depth analysis of the signals considered. Complex or sophisticated methods do not always bring the desired results. The TFBG spectrum is a specific signal in which the cut-off wavelength shifts with a change in the refractive index. It seems that detecting this place in the fundamental domain, i.e., wavelength, gives the best results in determining the SRI. This requires estimation of the local characteristics of the signal.