Obtain the F.S expression for the waveform shown in the figure,

Solution:

$ C_n=\frac{1}{T_0} \int_t^{t+T_0} x(t) \mathrm{e}^{-j n \omega_0 t} \mathrm{~d} t\\ $

$ =\frac{1}{2 \pi} \int_0^{2 \pi} x(t) \mathrm{e}^{-j n t} \mathrm{~d} t\\ $

$ \begin{aligned} & =\frac{1}{2 \pi}\left(\int_0^\pi \mathrm{e}^{-j n t} \mathrm{~d} t-\int_\pi^{2 \pi} 2 \mathrm{e}^{-j n t} \mathrm{~d} t\right) \\\\ & =\frac{1}{-2 \pi j n}\left(\left(\mathrm{e}^{-j n \pi}-1\right)-2\left(\mathrm{e}^{-j n …