PLEASE ANSWER $4,5,6$ NOT $1,2,3$

Questions $($Answers of these Qs can be included in items $($c$)$ and $($d$)$ of the ethical

questions below$)$

$(1)$ Write out the analytic solution $($refer to the solution of HW $2,$ Problem $1)$

of the Fourier Cosine and Sine Series Coefficients a$\_(0)($if any$),$ a$\_($n$)$ and b$\_($n$)($if any$)$

of g$\_($p$)($t$)$ given in the problem $($see the attached sketch above$).$

$(2)$ Calculate and show the FS Coefficients up to $11^($th $)$ harmonics a$\_(1),$a$\_(2),$a$\_(3),--,$a$\_(11)$

along with their respective frequencies.

$(3)$ Plot the given g$\_($p$)($t$)$ for to $+2\mathrm{.}5$sec for the later comparison purpose.

$(4)$ Plot the time domain plots for the results of approximation of g$\_($p$)($t$)$ for $5$ cases

respectively for the time duration $(-2\mathrm{.}5$ sec to $+2\mathrm{.}5$sec$).$

Cases: Summed up to $3$ harmonics, $5$ harmonics, $7$ harmonics, $9$ harmonics, and

$11$ harmonics.

$(5)$ Compare with the plot of original g$\_($p$)($t$)$ for each case above. Then Discuss on the

Accuracy of approximations per the cases of more harmonics added up$.$ It can

include discussion and comparison of peak magnitude, time spread or shifting,

overall shape of the plots, etc.

$(6)$ Using the coefficients you found up to $11$ harmonics, calculate the total average

power $($normalized to $1$ ohm load$)$ per respective cases. Then compare and discuss

on the difference.