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Three analog signals, having bandwidths 1200 Hz, 600 Hz, 600 Hz are sampled at their Nyquist rates, encoded with 12 bit words, and time division multiplexed. The bit rate for the multiplexed signal is
- a)115.2 kbps
- b)28.8 kbps
- c)57.6 kbps
- d)38.4 kbps
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three analog signals, having bandwidths 1200 Hz, 600 Hz, 600 Hz are sa...
The total message bandwidth = 1200 Hz + 600 Hz + 600 Hz = 2400 Hz
Sampling frequency = 4800 samples/sec.
Hence, Bit rate = 4800 x 12
57.6 kbps.Most Upvoted Answer
Three analog signals, having bandwidths 1200 Hz, 600 Hz, 600 Hz are sa...
Given:
Three analog signals with bandwidths of 1200 Hz, 600 Hz, and 600 Hz are sampled at their Nyquist rates, encoded with 12-bit words, and time division multiplexed.
To find:
The bit rate for the multiplexed signal.
Solution:
Step 1: Calculate the Nyquist rate for each signal
The Nyquist rate is twice the bandwidth of the signal.
Nyquist rate for the first signal = 2 * 1200 Hz = 2400 samples per second
Nyquist rate for the second signal = 2 * 600 Hz = 1200 samples per second
Nyquist rate for the third signal = 2 * 600 Hz = 1200 samples per second
Step 2: Calculate the total number of bits per second for each signal
The number of bits per sample is given as 12 bits.
Number of bits per second for the first signal = 2400 samples per second * 12 bits = 28,800 bits per second
Number of bits per second for the second signal = 1200 samples per second * 12 bits = 14,400 bits per second
Number of bits per second for the third signal = 1200 samples per second * 12 bits = 14,400 bits per second
Step 3: Calculate the total bit rate for the multiplexed signal
The bit rate for the multiplexed signal is the sum of the bit rates of all three signals.
Total bit rate = 28,800 bits per second + 14,400 bits per second + 14,400 bits per second = 57,600 bits per second
Therefore, the bit rate for the multiplexed signal is 57.6 kbps (kilobits per second), which corresponds to option C.
Three analog signals with bandwidths of 1200 Hz, 600 Hz, and 600 Hz are sampled at their Nyquist rates, encoded with 12-bit words, and time division multiplexed.
To find:
The bit rate for the multiplexed signal.
Solution:
Step 1: Calculate the Nyquist rate for each signal
The Nyquist rate is twice the bandwidth of the signal.
Nyquist rate for the first signal = 2 * 1200 Hz = 2400 samples per second
Nyquist rate for the second signal = 2 * 600 Hz = 1200 samples per second
Nyquist rate for the third signal = 2 * 600 Hz = 1200 samples per second
Step 2: Calculate the total number of bits per second for each signal
The number of bits per sample is given as 12 bits.
Number of bits per second for the first signal = 2400 samples per second * 12 bits = 28,800 bits per second
Number of bits per second for the second signal = 1200 samples per second * 12 bits = 14,400 bits per second
Number of bits per second for the third signal = 1200 samples per second * 12 bits = 14,400 bits per second
Step 3: Calculate the total bit rate for the multiplexed signal
The bit rate for the multiplexed signal is the sum of the bit rates of all three signals.
Total bit rate = 28,800 bits per second + 14,400 bits per second + 14,400 bits per second = 57,600 bits per second
Therefore, the bit rate for the multiplexed signal is 57.6 kbps (kilobits per second), which corresponds to option C.
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