Given a rectangular pulse as shown in Figure 13-4, with amplitude A, width \(T\), and period \(T_{0}\), we can compute and plot the coefficients in the corresponding Fourier series. If we allow \(T_{\mathrm{o}}\) to increase to infinity, the waveform is a single pulse and the Fourier series approaches a scaled version of the Fourier transform. To see this graphically, use MATLAB to create the following series of plots. Let \(A=5, T=1\), and \(T_{0}=2\). Compute the Fourier series coefficients for \(n=0,1,2, \ldots 10 T_{0}\). Create a stem plot of ( \(a_{n} \times T_{0}\) ) on the vertical axis versus the \(\left(n / T_{0}ight)\) on the horizontal axis. Increment \(T_{0}\) by one and repeat the stem plot. Create plots up until \(T_{0}=20\) and comment on the behavior of the results. Now compute the Fourier transform of \(f\) \((t)=A[u(t+T / 2)-u(t-T / 2)]\). Evaluate \(F(\omega)\) for \(\omega=0\) to \(20 \pi \mathrm{rad} / \mathrm{s}\). On the same axes as your final stem plot, plot \(2 F(\omega)\) versus \(\omega / 2 \pi\). Comment on the results.