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A black and white television picture may be viewed as consisting of approximately 3x105 elements, each of which may occur one of 10 distinct brightness levels with equal probability. Transmission rate is 30 picture frames/ second and SNR is 30 dB. Then the minimum bandwidth required to support the transmission of the resulting video signal is MHz
Correct answer is '3'. Can you explain this answer?
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A black and white television picture may be viewed as consisting of ap...
The information in each element is log210 bits. The information in each picture is [31og210]x105 bits. The transmitted information rate is
[9 log210] x106bits / second.
The channel must have this capacity. From the information capacity theorem,
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A black and white television picture may be viewed as consisting of ap...
Given information:
- Black and white television picture consists of approximately 3x105 elements
- Each element may occur one of 10 distinct brightness levels with equal probability
- Transmission rate is 30 picture frames/second
- SNR is 30 dB
To find:
- Minimum bandwidth required to support the transmission of the resulting video signal
Solution:
Step 1: Calculate the number of bits per frame
- Each element can occur one of 10 distinct brightness levels, so it can be represented by 4 bits (2^4 = 10).
- Therefore, each frame consists of 3x105 x 4 = 12x105 bits.
Step 2: Calculate the total number of bits per second
- The transmission rate is 30 picture frames/second.
- Therefore, the total number of bits per second is 30 x 12x105 = 3.6x107 bits/second.
Step 3: Calculate the minimum bandwidth required
- The SNR is 30 dB, which means the signal power is 1000 times greater than the noise power (since SNR = 10 log10 (signal power / noise power)).
- Therefore, the noise power is 1/1000 of the signal power.
- The Shannon-Hartley theorem states that the maximum data rate of a channel is given by C = B log2 (1 + S/N), where C is the capacity of the channel, B is the bandwidth, S is the signal power, and N is the noise power.
- Rearranging this equation, we can find the minimum bandwidth required: B = C / log2 (1 + S/N).
- Plugging in the values we have, we get B = 3.6x107 / log2 (1 + 1000) = 3 MHz.
Therefore, the minimum bandwidth required to support the transmission of the resulting video signal is 3 MHz.
- Black and white television picture consists of approximately 3x105 elements
- Each element may occur one of 10 distinct brightness levels with equal probability
- Transmission rate is 30 picture frames/second
- SNR is 30 dB
To find:
- Minimum bandwidth required to support the transmission of the resulting video signal
Solution:
Step 1: Calculate the number of bits per frame
- Each element can occur one of 10 distinct brightness levels, so it can be represented by 4 bits (2^4 = 10).
- Therefore, each frame consists of 3x105 x 4 = 12x105 bits.
Step 2: Calculate the total number of bits per second
- The transmission rate is 30 picture frames/second.
- Therefore, the total number of bits per second is 30 x 12x105 = 3.6x107 bits/second.
Step 3: Calculate the minimum bandwidth required
- The SNR is 30 dB, which means the signal power is 1000 times greater than the noise power (since SNR = 10 log10 (signal power / noise power)).
- Therefore, the noise power is 1/1000 of the signal power.
- The Shannon-Hartley theorem states that the maximum data rate of a channel is given by C = B log2 (1 + S/N), where C is the capacity of the channel, B is the bandwidth, S is the signal power, and N is the noise power.
- Rearranging this equation, we can find the minimum bandwidth required: B = C / log2 (1 + S/N).
- Plugging in the values we have, we get B = 3.6x107 / log2 (1 + 1000) = 3 MHz.
Therefore, the minimum bandwidth required to support the transmission of the resulting video signal is 3 MHz.
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A black and white television picture may be viewed as consisting of approximately 3x105 elements, each of which may occur one of 10 distinct brightness levels with equal probability. Transmission rate is 30 picture frames/ second and SNR is 30 dB. Then the minimum bandwidth required to support the transmission of the resulting video signal is MHzCorrect answer is '3'. Can you explain this answer?
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