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Three message signals each band limited to 10 kHz, 10 kHz, and 5 KHz are transmitted through a channel using frequency division multiplexing. The modulation techniques used are any, D513-SC, SSB respectively. The guard band is 2 KHz. Band width of the channel is
  • a)
    49 kHz
  • b)
    45 kHz 
  • c)
    53 kHz   
  • d)
    57 kHz
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Three message signals each band limited to 10 kHz, 10 kHz, and 5 KHz a...
BW after AM modulation = 2 x 10 = 20 KHz
BW after DSS-SC modulation = 2 x10 = 20 KHz BW after SSB modulation = 5 KHz
Guard band width = 2 x 2k=4 k
∴ Total BW after frequency multiplexing = 49 KHz
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Most Upvoted Answer
Three message signals each band limited to 10 kHz, 10 kHz, and 5 KHz a...
Solution:

Given:

Bandwidth of the first message signal = 10 kHz

Bandwidth of the second message signal = 10 kHz

Bandwidth of the third message signal = 5 kHz

Guard band = 2 kHz

Modulation used for the first message signal = Any modulation

Modulation used for the second message signal = D513-SC

Modulation used for the third message signal = SSB

To find: Bandwidth of the channel

Frequency Division Multiplexing (FDM):

FDM is a technique of combining multiple signals and transmitting them over a single channel. In FDM, each message signal is modulated with a carrier signal of different frequencies. The modulated signals are then combined and transmitted over a single channel.

The given system uses FDM to transmit three message signals.

Bandwidth Calculation:

The bandwidth of the channel is given by the sum of the bandwidths of all the modulated signals and the guard band.

Bandwidth of the first modulated signal:

As the modulation used for the first message signal is any modulation, we assume that it is modulated using AM (Amplitude Modulation).

The bandwidth of AM is given by the formula,

BAM = 2 × (fm + fc)

where,

fm = Maximum frequency component of the message signal

fc = Carrier frequency

Here, fc = 0 Hz (baseband signal)

fm = 10 kHz (Given)

BAM = 2 × (10 kHz + 0 Hz) = 20 kHz

Bandwidth of the second modulated signal:

The modulation used for the second message signal is D513-SC (Double Sideband with 5 kHz carrier).

The bandwidth of D513-SC is given by the formula,

BD513-SC = 2 × (fm + fc)

where,

fm = Maximum frequency component of the message signal

fc = Carrier frequency

Here, fc = 5 kHz (Given)

fm = 10 kHz (Given)

BD513-SC = 2 × (10 kHz + 5 kHz) = 30 kHz

Bandwidth of the third modulated signal:

The modulation used for the third message signal is SSB (Single Sideband).

The bandwidth of SSB is equal to the bandwidth of the message signal.

Here, the maximum frequency component of the message signal is 5 kHz.

Bandwidth of SSB = 5 kHz

Total bandwidth of the modulated signals:

Total bandwidth of the modulated signals = BAM + BD513-SC + Bandwidth of SSB

= 20 kHz + 30 kHz + 5 kHz

= 55 kHz

Total bandwidth of the channel:

Total bandwidth of the channel = Total bandwidth of the modulated signals + Guard band

= 55 kHz + 2 kHz

= 57 kHz

Therefore, the bandwidth of the channel is 57 kHz.

Hence, option (D) is the correct answer.
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Three message signals each band limited to 10 kHz, 10 kHz, and 5 KHz are transmitted through a channel using frequency division multiplexing. The modulation techniques used are any, D513-SC, SSB respectively. The guard band is 2 KHz. Band width of the channel isa)49 kHzb)45 kHzc)53 kHzd)57 kHzCorrect answer is option 'A'. Can you explain this answer?
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