GATE 2025 EC – Question 28
Consider a message signal $m(t)$ which is bandlimited to $[-W,W]$, where $W$ is in Hz. Consider the following two modulation schemes for the message signal:
- Double sideband-suppressed carrier (DSB-SC): $f_{DSB}(t)=A_c\,m(t)\cos(2\pi f_ct)$
- Amplitude modulation (AM): $f_{AM}(t)=A_c\big(1+\mu\,m(t)\big)\cos(2\pi f_ct)$
Here, $A_c$ and $f_c$ are the amplitude and frequency (in Hz) of the carrier, respectively. In the case of AM, $\mu$ denotes the modulation index.
Consider the following statements:
(i) An envelope detector can be used for demodulation in the DSB-SC scheme if $m(t)>0$ for all $t$.
(ii) 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?
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Show answer and explanation
Correct answer: (A) (i) is TRUE; (D) (ii) is FALSE
Explanation
(i) The envelope of the DSB-SC signal is $A_c|m(t)|$, which equals $A_cm(t)$ when $m(t)>0$, so the message is recovered: TRUE. (ii) An AM envelope detector only needs $1+\mu m(t)>0$ (no over-modulation). $m(t)$ may go negative as long as $\mu|m(t)|<1$, so "only if $m(t)>0$" is FALSE.