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Find the minimum channel bandwidth ( in kHz) required to transmit an 8-ary PSK signal with each bit duration of 15.6μs.
- a)21.1
- b)21.2
- c)21.4
- d)21.6
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Find the minimum channel bandwidth ( in kHz) required to transmit an ...
We have, bit rate,
Rb = 1/Tb = 1/15.6×10-6 = 64.1kbps
Now, channel bandwidth required for M-array PSK is B = 2Rb/log2M
Minimum Channel bandwidth required for an M-PSK is Rb/log2M
Here, M = 8
⇒ B = 64.1k/log28 = 21.4kHz
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Community Answer
Find the minimum channel bandwidth ( in kHz) required to transmit an ...
To find the minimum channel bandwidth required to transmit an 8-ary PSK signal, we need to consider the bit rate and modulation scheme. The given information states that the bit duration is 15.6μs, which means the bit rate is 1/15.6μs.
1. Bit Rate Calculation:
Bit rate = 1 / bit duration
Bit rate = 1 / 15.6μs
Bit rate = 64.1 kbps
2. Modulation Scheme:
The modulation scheme used is 8-ary PSK, which means there are 8 different phase shifts representing 8 different symbols. Each symbol carries 3 bits of information.
3. Symbol Rate Calculation:
Symbol rate = Bit rate / number of bits per symbol
Symbol rate = 64.1 kbps / 3
Symbol rate = 21.4 kbaud
4. Nyquist Bandwidth Calculation:
Nyquist bandwidth is calculated using the formula:
Nyquist bandwidth = 2 * symbol rate
Nyquist bandwidth = 2 * 21.4 kHz
Nyquist bandwidth = 42.8 kHz
5. Minimum Channel Bandwidth Calculation:
For efficient transmission, the minimum channel bandwidth should be slightly greater than the Nyquist bandwidth.
In this case, the minimum channel bandwidth required to transmit the 8-ary PSK signal with a bit duration of 15.6μs is 42.8 kHz.
Therefore, the correct answer is option 'C' (21.4 kHz).
1. Bit Rate Calculation:
Bit rate = 1 / bit duration
Bit rate = 1 / 15.6μs
Bit rate = 64.1 kbps
2. Modulation Scheme:
The modulation scheme used is 8-ary PSK, which means there are 8 different phase shifts representing 8 different symbols. Each symbol carries 3 bits of information.
3. Symbol Rate Calculation:
Symbol rate = Bit rate / number of bits per symbol
Symbol rate = 64.1 kbps / 3
Symbol rate = 21.4 kbaud
4. Nyquist Bandwidth Calculation:
Nyquist bandwidth is calculated using the formula:
Nyquist bandwidth = 2 * symbol rate
Nyquist bandwidth = 2 * 21.4 kHz
Nyquist bandwidth = 42.8 kHz
5. Minimum Channel Bandwidth Calculation:
For efficient transmission, the minimum channel bandwidth should be slightly greater than the Nyquist bandwidth.
In this case, the minimum channel bandwidth required to transmit the 8-ary PSK signal with a bit duration of 15.6μs is 42.8 kHz.
Therefore, the correct answer is option 'C' (21.4 kHz).
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Find the minimum channel bandwidth ( in kHz) required to transmit an 8-ary PSK signal with each bit duration of 15.6μs.a)21.1b)21.2c)21.4d)21.6Correct answer is option 'C'. Can you explain this answer?
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