Solution:

$C_n=\frac{1}{T_0} \int_{-\frac{T_0}{2}}^{\frac{T_0}{2}} x(t) \mathrm{e}^{-j n \omega_0 t} \mathrm{~d} t$

$=\frac{1}{T_0} \int_{-\frac{T_0}{2}}^{\frac{T_0}{2}} \delta(t) \mathrm{e}^{-j n \omega_0 t} \mathrm{~d} t$

$\text { Since: } \mathrm{x}(\mathrm{t}) \cdot \delta(t)=\mathrm{x}(0) \cdot \delta(t) \text { and area under impulse is unity }$

$ =\frac{1}{T_0} \int_{-\frac{T_0}{2}}^{\frac{T_0}{2}} \delta(t) \mathrm{e}^0 \mathrm{~d} t …