## 3 Results and Discussion  
Data processing, based on the DFT algorithm, allowed for the sequence of samples of signal \(x(k)\), recorded in the time domain, to be described by a set of spectral components \(X(n)\) in the frequency domain. The number of spectral components in the frequency domain was equal to the number of samples \(N\) in the time domain, where the selected number of samples \(N\) was the integer power of 2. Given that DFT, which is defined by Equation (1), yielded results in complex form, the temperature profile of each pixel in the sequence of recorded thermal images could be described by the corresponding amplitude and phase characteristic in the frequency domain. These characteristics were used to generate corresponding amplitude (PT method) and phase (PPT method) maps, which made the defects more easily detectable than in the case of analysis of the original thermal image. \[X(n)=\sum_{k=0}^{N-1}x(k)e^{-i\frac{2\pi}{N}nk}n=0,1,\ldots,N-1. \tag{1}\]  
To assess the depth of a defect, it is necessary to process data recorded at different sampling frequencies. In the specific case, this was achieved by pre-programmed extraction of suitable frames from the basic sequence recorded at a camera sampling frequency of \(f_{\mathrm{s}}\) = 30 frames per second. Two procedures were followed. In the first procedure (Procedure A), 64 frames were extracted in the order: \(k\) = 3, 6, 9, 12, 15, 18, 21 and 24, using the loop FOR \(i\) = \(k_{0}\):\(k\):(\(k_{0}\) + \(k\):63). This resulted in the minimum sampling frequency of \(f_{\mathrm{min}}\) = 30/24 samples per second. For each pixel selected in this manner with 64 frames, vector \(x(k)\) was generated and used in the DFT described by Equation (1). A total of 1617 frames were captured during the experiment. Keeping in mind that at \(k\) = 24 at least \(1\) + 24 \(\times\) 63 = 1513 are required, any further frequency reduction was not possible. On the other hand, if only 32 frames were used, a smaller number of spectral components would be obtained (i.e., the resolution in the frequency domain would be poorer). To enhance resolution, in the second procedure (Procedure B) the number of samples \(N\) was increased, but without adding information by selecting additional frames from the basic sequence of all recorded frames. Instead, \"zero frames\" were introduced (i.e., the values of all pixels in the corresponding matrix were equal to zero). This meant that a sample vector was generated each time and its every \(k\)-th term, beginning with the first, had the value of the corresponding pixel within the sequence of the 64 frames selected from the basic sequence, as in the case of Procedure A. All other terms were zero. The total number of terms \(N\) of the vector generated in this way was equal to the minimum value of the power of 2, which ensured that the pixel values of all frames extracted from the basic sequence by means of the previously-mentioned FOR NEXT loop were stored. It follows from Equation (1) that all samples of signal \(x(k)\), recorded in the time domain, participate in the computation of all spectral components \(X(n)\) in the frequency domain. The introduction of zero frames had the indirect effect of sampling frequency reduction. Namely, the frequency of appearing frames that participate with their pixel values in the computation of spectral components \(X(n)\) corresponds to the desirable sampling frequency. For example, at \(k\) = 3 the frequency of appearing frames whose elements differed from zero was lower by a factor of three. In order to facilitate assessment of the changes upon heating of the test sample, the variation in intensity in areas whose size was \(16\times 16\) pixels, denoted by B, C, D, E and Sa in Figure 2, were