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An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is ________
Correct answer is '0.25'. Can you explain this answer?
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An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communicat...
To determine the roll-off factor of a pulse with a raised cosine spectrum, we need to consider the bandwidth of the channel, the bit rate, and the modulation scheme used. Let's break down the information provided in the question and explain how to arrive at the correct answer.
Given Information:
- Band-pass channel: 500 Hz - 2000 Hz
- Modem bit rate: 4800 bits/s
- Modulation scheme: 16-QAM
1. Determine the Bandwidth:
The bandwidth of the band-pass channel is given as 500 Hz to 2000 Hz. The total bandwidth can be calculated by subtracting the lower frequency from the upper frequency:
Bandwidth = 2000 Hz - 500 Hz = 1500 Hz
2. Determine the Symbol Rate:
In 16-QAM, each symbol represents 4 bits (2^4 = 16). Therefore, the symbol rate can be calculated by dividing the bit rate by the number of bits per symbol:
Symbol rate = 4800 bits/s / 4 bits/symbol = 1200 symbols/s
3. Determine the Roll-off Factor:
The roll-off factor, denoted by α, is a measure of the excess bandwidth of a pulse with a raised cosine spectrum. It determines how much the spectrum extends beyond the ideal bandwidth. The relationship between the roll-off factor and the excess bandwidth is given by the formula:
Excess bandwidth = (1 + α) * Symbol rate
In this case, we know the excess bandwidth is equal to the total bandwidth, as the pulse with a raised cosine spectrum utilizes the entire frequency band. Therefore, we can set up the equation as follows:
1500 Hz = (1 + α) * 1200 symbols/s
4. Solve for the Roll-off Factor:
Divide both sides of the equation by 1200:
1500 Hz / 1200 symbols/s = 1 + α
Simplify the equation:
1.25 = 1 + α
Subtract 1 from both sides of the equation:
1.25 - 1 = α
Simplify the equation to find the roll-off factor:
α = 0.25
Hence, the roll-off factor of the pulse with a raised cosine spectrum is 0.25.
Given Information:
- Band-pass channel: 500 Hz - 2000 Hz
- Modem bit rate: 4800 bits/s
- Modulation scheme: 16-QAM
1. Determine the Bandwidth:
The bandwidth of the band-pass channel is given as 500 Hz to 2000 Hz. The total bandwidth can be calculated by subtracting the lower frequency from the upper frequency:
Bandwidth = 2000 Hz - 500 Hz = 1500 Hz
2. Determine the Symbol Rate:
In 16-QAM, each symbol represents 4 bits (2^4 = 16). Therefore, the symbol rate can be calculated by dividing the bit rate by the number of bits per symbol:
Symbol rate = 4800 bits/s / 4 bits/symbol = 1200 symbols/s
3. Determine the Roll-off Factor:
The roll-off factor, denoted by α, is a measure of the excess bandwidth of a pulse with a raised cosine spectrum. It determines how much the spectrum extends beyond the ideal bandwidth. The relationship between the roll-off factor and the excess bandwidth is given by the formula:
Excess bandwidth = (1 + α) * Symbol rate
In this case, we know the excess bandwidth is equal to the total bandwidth, as the pulse with a raised cosine spectrum utilizes the entire frequency band. Therefore, we can set up the equation as follows:
1500 Hz = (1 + α) * 1200 symbols/s
4. Solve for the Roll-off Factor:
Divide both sides of the equation by 1200:
1500 Hz / 1200 symbols/s = 1 + α
Simplify the equation:
1.25 = 1 + α
Subtract 1 from both sides of the equation:
1.25 - 1 = α
Simplify the equation to find the roll-off factor:
α = 0.25
Hence, the roll-off factor of the pulse with a raised cosine spectrum is 0.25.
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Community Answer
An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communicat...
Concept: By using raised cosine pulse bandwidth required for M-ary modulation is 
where α is called roll-off factor.
Application: Bandwidth = 2000 - 500 = 1500 Hz
Bandwidth required for 16 QAM
Rb(1+α ) = 1500 x 4 = 6000
(1+α) = 6000/4800
α = 0.25
where α is called roll-off factor.Application: Bandwidth = 2000 - 500 = 1500 Hz
Bandwidth required for 16 QAM
Rb(1+α ) = 1500 x 4 = 6000
(1+α) = 6000/4800
α = 0.25
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An ideal band-pass channel 500 Hz - 2000 Hz is deployed for communication. A modem is designed to transmit bits at the rate of 4800 bits/s using 16-QAM. The roll-off factor of a pulse with a raised cosine spectrum that utilizes the entire frequency band is ________Correct answer is '0.25'. Can you explain this answer?
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