## 4 Determination of Rasterization Parameter Values  
### FFT Transform  
The horizontal and vertical frequencies values can be determined by analyzing the spectrum of the recorded video signal (or the revealing signal). Using the FFT transform, it  
Figure 4: (a) Amplitude spectrum of the test signal (window of MS Word editor) and magnification of its fragments corresponding to the (b) horizontal and (c) vertical sync frequencies. Figure 5: Magnification of the fragments of the amplitude spectrum corresponding to the (a) horizontal and (b) vertical sync frequencies. is possible to determine the position of the spectrum lines corresponding to the image line length and their number in the image [35; 36; 37]. The resolution of the FFT transform is determined by the ratio of the sampling frequency \(f_{s}\) to the number of samples \(N\) being subject to analysis. \[\Delta_{f}=\frac{f_{s}}{N} \tag{1}\]  
As mentioned earlier, the operation of recreating the actual line length should be performed with accuracy to the fourth decimal place. In the case of, e.g., monitors operating in the modes and with the parameters specified in Table 1, let \(f_{H}\) denote the value of the horizontal synchronization frequency corresponding to the actual length of the image line, \(f_{H1}\) denote the value of the horizontal synchronization frequency corresponding to the actual length of the image line reduced about value 0.01, and \(f_{H2}\) denote the value of the horizontal synchronization frequency corresponding to the actual image line length increased about value 0.01. According to the formula:  
\[\Delta f_{H}=f_{H1}-f_{H}=f_{H}-f_{H2}, \tag{2}\]  
the accuracy values of determining the horizontal synchronization frequency were obtained (Table 4). Taking into account the above-specified accuracy of determining the horizontal synchronization frequency, it is possible to determine the required number of signal samples necessary to determine the amplitude spectrum by using the FFT (Table 5). Based on Table 5, it can be concluded that the use of a simple FFT transform to determine the values of raster parameters would require the use of large computing resources and operating on very large data sets. It should be additionally taken into account that the performance of FFT calculations at a certain level of accuracy requires the use of a representation of numbers in the double (64-bit) format, so the data sets in the PC memory used for calculations are 8 times larger than the required number of samples presented in Table 5. It should be noted that the Fourier transform applies to the entire frequency range of the analyzed signal. In the most cases, this is an uneconomical process. In addition, the so-called frequency resolution of the Fourier transform, i.e., the smallest detectable difference between the two spectral components, is insufficient. Very often, \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Operating Mode** & **Sampling Rate** & **Real Number of** & \(f_{H}\) & \(f_{H1}\) & \(f_{H2}\) & \(\Delta f_{H}\) \\
**of Display** & **[MHz]** & **Pixels in the Line** & **[Hz]** & **[Hz]** & **[Hz]** & **[Hz]** \\ \hline
640 \(\times\) 480/60 Hz & 31.25 & 993.0408 & 31,468.9991 & 31,469.3160 & 31,468.6822 & 0.3169 \\ \hline
1366 \(\times\) 768/60 Hz & 125.00 & 2619.8860 & 23,855.9998 & 23,856.0909 & 23,855.9088 & 0.0911 \\ \hline
1600 \(\times\) 900/60 Hz & 125.00 & 2083.3333 & 60,000.0010 & 60,000.2890 & 59,999.7130 & 0.2880 \\ \hline
1920 \(\times\) 1080/60 Hz & 250.00 & 3703.7037 & 67,500.0001 & 67,500.1823 & 67,499.8178 & 0.1823 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Determination of the required spectrum resolution for the FFT.