
2.6.1.4 Fourier integral
Problem:
Find the Fourier image \( F[f(x)](v) \)
\( =\int_{-\infty}^{+\infty} f(t) e^{-i v t} d t \) of function \( f(t) \), using equalities
\( F[ \) rect \( t](v)=\operatorname{sinc} \frac{v}{2} \) and \( F[\Lambda(t)](v)=\operatorname{sinc}^{2} \frac{v}{2} \).
The graph of function \( f(t) \) consists a polygonal chain, connecting points \( A, B, C \) and \( D \), as well as from parts of the \( \mathrm{x} \)-axis (to the left of \( A \) and to the right of \( D \) ).
\begin{tabular}{|c|c|c|c|}
\hline\( A \) & \( B \) & \( C \) & \( D \) \\
\hline\( (-1,1) \) & \( (1,-2) \) & \( (4,-2) \) & \( (6,1) \) \\
\hline
\end{tabular}