$3.($a$)$ Write down the Fourier series of a periodic signal $\backslash (\backslash$mathrm$\{$F$\}(\backslash$mathrm$\{$t$\})\backslash )$ of period $\backslash (\backslash$mathrm$\{$T$\}(10)\backslash ).$

$($b$)$ Derive the discrete version of the Fourier series, assuming that N discrete data with equal sampling time are obtained $(10).$