Plot the time domain plots for the results of approximation of gp $($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.

$*$Problem $2($below is identical to the directions given in the Problem $2$ later$)$

A$.$ Problem statement $($write out the given problem$)$

B$.$ Analytically derive an expression for the modulated signal S$($t$).($See details given

in Problem $2)$

C$.$ Using Matlab plot, show the time domain waveforms of given m$($t$),$S$($t$)$s with

different k$\_($a$)=0\mathrm{.}5,0\mathrm{.}95$ as well as k$\_($a$)=0\mathrm{.}85($given$)$ up to $1[$sec$].$

D$.$ Determine the spectra of the message signal M$($f$)$ and modulated signal S$($f$)$k$\_($a$)$ k$\_($a$)$ towards time domain

waveforms as well as frequency domain spectra