PROBLEM $2\mathrm{.}3(20$ Points$)$ Consider the signal

$y(t)=3+5sin(20t-0\mathrm{.}3)-4cos(60t)+2cos(80t-0\mathrm{.}2)$

$($a$)$ Sketch the discrete amplitude spectrum obtained from taking $20$ samples of $y(t)$ at sampling frequency $100$ Hz

$($b$)$ Sketch the discrete amplitude spectrum obtained from taking $24$ samples of $y(t)$ at sampling frequency $60$ Hz

$($c$)$ Sketch the discrete amplitude spectrum obtained from taking $18$ samples of $y(t)$ at sampling frequency $36$ Hz