$5)($a$)$ Draw a random PAM$-4$ waveform with NRZ pulse shape, average power of $1$ W and bit rate $40\backslash (\backslash$mathrm$\{$Mbit$\}/\backslash$mathrm$\{$s$\}\backslash ).$ Label the amplitude levels and symbol duration accordingly.

$[4$ marks$]$

$($b$)$ What is inter$-$symbol interference$($ISI$)?$ Illustrate it with a diagram.

$[4$ marks$]$

$($c$)$ The signal in $($a$)$ is transmitted through a $5$ km wire with attenuation $\backslash (2\backslash$mathrm$\{$~dB$\}/\backslash$mathrm$\{$km$\}\backslash )$ and the total noise power of the communication system is $0\mathrm{.}001$ W $.$ Determine if this PAM$-4$ signal can be successfully transmitted if the BER threshold is $\backslash (10^\{-4\}\backslash ).$

$[5$ marks$]$

$($d$)$ Show how one can reduce the total bit rate of the signal in $($a$)$ to ensure successful transmission through the system in $($c$).$

$[5$ marks$]$