Q$2)[40$p$]$ Given the following message and carrier signal

$m(t)=cos2000t+2cos6000t+cos10000t$

$c(t)=20cos320000t$

a$)$ Determine the Hilbert transform of $m(t).$

b$)$ Determine the Single Side Band $($SSB$)$ AM signal $u_{SSB}(t)$ which uses upper sideband.

c$)$ Plot the spectrum $U_{SSB}(f)$ of $u_{SSB}(t).$