Question

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): \[ f_{DSB}(t) = A_c m(t) \cos(2\pi f_c t) \] • Amplitude modulation (AM): \[ f_{AM}(t) = A_c \left( 1 + \mu m(t) \right) \cos(2\pi f_c t) \] 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?

• A. \( (i) \) is TRUE
• B. \( (i) \) is FALSE
• C. \( (ii) \) is TRUE
• D. \( (ii) \) is FALSE

Hint:

An envelope detector can demodulate AM signals effectively even when \( m(t) \) is negative, as long as it is bandlimited. In DSB-SC, the envelope detection requires \( m(t) \) to be positive for reliable demodulation.

Answer 1

The Correct Option is A, D

(i) An envelope detector can be used for demodulation in the DSB-SC scheme if \( m(t) > 0 \) for all \( t \):
This statement is true. For the DSB-SC scheme, the envelope of the signal can be used to recover the original message signal \( m(t) \). The envelope detector can work effectively when \( m(t) \) is positive for all time, ensuring the envelope follows the signal correctly.

(ii) An envelope detector can be used for demodulation in the AM scheme only if \( m(t) > 0 \) for all \( t \):
This statement is false. In AM, the envelope detector can be used to demodulate the signal regardless of whether \( m(t) \) is always positive. The envelope of the AM signal directly represents the message \( m(t) \), even if the message contains negative values, as long as it is bandlimited.

Therefore, the correct answers are (A) and (D).