Question $2$

A signal $m(t)$ is defined as

$m(t)=sin{c}^2(f_{m}t)$

The signal $m(t)$ is sampled using uniformly spaced impulses at a rate of $($a$)f_{m}Hz,($b$)2f_{m}Hz,($c$)4f_m$ Hz$.$

For each of the three cases:

Sketch the sampled signal

Sketch the spectrum of the sampled signal

Can you recover the signal $m(t)$ from the sampled signal

If the sampled signal is passed through an ideal low$-$pass filter of bandwidth $f_{m}Hz,$ sketch the spectrum of the output signal, and write its expression in time$-$domain.