In a transmitter the audio signal of frequency $ω_m$ is modulated by the carrier signal $ω_c$ and the band pass filter in it rejects the frequencies
- $ω_c$ and $ω_m$
- $ω_c - ω_m$ and $ω_c + ω_m$
- $ω_m$ and $2ω_c$
- $ω_c - ω_m$ and $ω_c $
- $ω_c + ω_m$ and $ω_m $
The Correct Option is
Solution and Explanation
In a transmitter, the audio signal of frequency \( \omega_m \) is modulated by the carrier signal of frequency \( \omega_c \). The modulation process generates a signal that contains three components:
- The carrier frequency \( \omega_c \),
- The upper sideband \( \omega_c + \omega_m \),
- The lower sideband \( \omega_c - \omega_m \).
The band-pass filter in the transmitter is used to select only the frequencies around the carrier frequency and reject the unwanted frequencies. This means that the filter will reject:
- The carrier frequency \( \omega_c \),
- The audio signal frequency \( \omega_m \),
- The frequencies \( \omega_c - \omega_m \) and \( \omega_c + \omega_m \), which correspond to the lower and upper sidebands of the modulated signal.
Thus, the band-pass filter will reject the frequencies \( \omega_c + \omega_m \) and \( \omega_m \), as those are not part of the intended modulated signal.
Correct Answer:
Correct Answer: (E) \( \omega_c + \omega_m \) and \( \omega_m \)
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