Consider a message signal $m(t)$ which is bandlimited to $[-W, W]$, where $W$ is in $\mathrm{Hz}$ . Consider the following two modulation schemes for the message signal:
- Double sideband-suppressed carrier (DSB-SC):
$$f_{D S B}(t)=A_{c} \: m(t) \cos \left(2 \pi f_{c} t\right)$$
- Amplitude modulation (AM):
$$f_{A M}(t)=A_{c}(1+\mu \: m(t)) \cos \left(2 \pi f_{c} t\right)$$
Here, $A_{c}$ and $f_{c}$ are the amplitude and frequency (in $\mathrm{Hz}$ ) of the carrier, respectively. In the case of $\mathrm{AM}, \mu$ denotes the modulation index.
Consider the following statements:
- An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.
- An envelope detector can be used for demodulation in the AM scheme only if $m(t)>0$ for all $t$.
Which of the following options is/are correct?
- $(i)$ is TRUE
- $(i)$ is FALSE
- $(ii)$ is TRUE
- $(ii)$ is FALSE
