$2$ The message signal $\backslash (\backslash$mathrm$\{$m$\}(\backslash$mathrm$\{$t$\})\backslash )$ has the Fourier transform shown in the Fig $1.$ This message signal is applied to the system shown in the Fig $2$ to generate the signal $\backslash ($ y$($t$)\backslash ).$

Fig. $1$

Fig. $2$

a$.$ Plot the spectrum of the signal at the output of the first multiplier

b$.$ Plot the spectrum of the signal at the output of the HPF

c$.$ Plot the spectrum of the signal at the output of the second multiplier

d$.$ Plot the spectrum of the signal $\backslash ($ y$($t$)\backslash )$

e$.$ The output signal $\backslash ($ y$($t$)\backslash )$ is given as input instead of $\backslash ($ m$($t$)\backslash )$ to the circuit given in Fig $2,$ then what will be the signal you will get as an output to the LPF$?$

$\backslash ([10][\backslash$mathrm$\{$CO$\}01,02][\backslash$mathrm$\{$BTL$\}3]\backslash )$