2.6.2.7 Trigonometric Fourier series

Problem: Expand function \( f(x) \) into Fourier series in the form of a superposition of simple harmonics, given on the segment line \( [-T / 2, T / 2] \). Plot: 1. Amplitude and phase spectra; 2. Graphs of partial sums of the Fourier series \( S_{3}(x), S_{10}(x), S_{20}(x), S_{100}(x) \). The values of parameters \( T, h, p \) and \( q \) are given in the table: \begin{tabular}{|c|c|c|c|} \hline\( T \) & \( h \) & \( p \) & \( q \) \\ \hline 2 & -2 & 2 & -1 \\ \hline & \( p \), & \begin{tabular}{l} \( / 2 \leq \) \\ \( -T / 4 \) \end{tabular} & \\ \hline & \( 2-\frac{2 l}{T} \) & & \\ \hline \end{tabular}