An interactive online graphing calculator to visualize a pulse \( f(t) \) and its Fourier transform \( F(\omega) \) is presented. \( t \) is the time and \( \omega \) is the angular frequency.
The Fourier of \( f(t) \) is defines by
\[ F(\omega) = \int_{-\infty}^{+\infty} f(t) e^\left( - j \omega t\right) dt \\
= \int_{-T/2}^{+T/2} 1 \cdot e^\left( - j \omega t\right) dt \\
= \left[ \dfrac{ e^\left( - j \omega t \right)}{-j \omega} \right]^{T/2}_{-T/2}
\]
Evaluate and simplify to obtain
\[ F(\omega) = \dfrac{\sin(\omega(T/2))}{\omega/2}
\]
T =