Q$.\backslash ((\backslash$mathbf$\{100\}\backslash$mathrm$\{$pts$\})\backslash )$ The signal $\backslash (\backslash$omega$(\backslash$mathrm$\{$t$\})\backslash )$ given below will be input to a PCM system to have a digital representation. The signal $\backslash (\backslash$omega$($t$)\backslash )$ has nonzero values only from $0$ to $21$ milliseconds as can be seen from the graph. The spectrum for $\backslash (\backslash$omega$($t$)\backslash )$ is $\backslash (\backslash$mathrm$\{$W$\}(\backslash$mathrm$\{$f$\})\backslash )$ which is also shown below. The PCM system is using the maximum sampling period allowed by the Sampling Theorem and it has a PCM Accuracy of $12\mathrm{.}5\backslash \%.$

a$.$ Write the sampling time instants for the given signal.

b$.$ Write the sample amplitudes at the sampling time instants provided on part a$.$

c$.$ Write the Quantization output for the samples obtained on part b by using the minimum allowed number of quantization levels.

d$.$ Write the Binary output representing $\backslash (\backslash$omega$(\backslash$mathrm$\{$t$\})\backslash )$ by using the quantization output obtained on part $\backslash (\backslash$mathbf$\{$c$\}\backslash ).$