A message signal $\backslash ($ m$($t$)\backslash )($shown below$)$ is sampled and quantized using a uniform quantizer in PCM$.$ The required output SNR is at least $36$ dB $.$

$($a$)$ Find the required minimum number of bits per sample.

$($b$)$ Assume the system transmission bandwidth $\backslash (\backslash$mathrm$\{$B$\}\_\{\backslash$mathrm$\{$T$\}\}=\backslash$mathrm$\{$C$\}=23\backslash$mathrm$\{$MHz$\}\backslash ),$ If raisedcosine pulses with roll$-$off $\backslash (\backslash$alpha$=0\mathrm{.}3\backslash )$ are used, What is the maximum data rate of the system?

$($c$)$ What is the corresponding sampling rate f needed for satisfactory transmission of the data in part $($b$)?$