A sinusoidal carrier wave with amplitude $A_{c}$ and frequency $f_{c}$ is amplitude modulated with a message signal $m(t)$ having frequency $0 < f_{m} \ll f_{c}$ to generate the modulated wave $s(t)$ given by
$$ s(t) = A_{c} [1+m(t)] \cos (2 \pi f_{c}t) $$
The message signal that can be retrieved completely using envelope detection is ___________
- $m(t) = 0.5 \cos (2 \pi f_{m} t)$
- $m(t) = 1.5 \sin (2 \pi f_{m} t)$
- $m(t) = 2 \sin (4 \pi f_{m} t)$
- $m(t) = 2 \cos (4 \pi f_{m} t)$