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The problem involves calculating the channel capacity of a telephone line based on its bandwidth and signal-to-noise ratio. It also includes a comparison between an analog telephone line and a digital telephone line using logarithmic PCM encoding.
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To calculate the channel capacity of the analog telephone line, we use the formula C = B * log2(1 + SNR), where C is the channel capacity in bits per second, B is the bandwidth in Hz, and SNR is the signal-to-noise ratio. By converting the SNR from dB to a linear scale, we find that the channel capacity is approximately 21,312 bits per second.
For the digital telephone line, we use the same formula but with a different SNR calculation. Using logarithmic PCM encoding with 12 bits, we approximate the SNR as 82.8752. With a bandwidth of 3800 Hz, the channel capacity is approximately 23,004 bits per second.
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