GATE EC 2025 Set 1 Q18 — Analog Communications

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:

1. An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.
2. 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?