A$2\mathrm{.}5.$ Consider the periodic function that is defined by $$ f$($t$)=04$t$<2($t $+2)2$t$<0$ t $20$t$<202$t$<4$ f$($t $+8)$ for all t$.($a$)$ Produce a good quality graph of this function, showing at least three periods. $($b$)$ Calculate the Fourier series for f$.($c$)$ Use Python $($or an alternative$)$ to plot s$4,$s$6,$s$8$ on the same graph, where sN$($t$)$ is the truncation of the Fourier series at the Nth term. $($d$)$ Discuss the convergence of this series as N $$ $.$ Is there any overshoot?