GATE EC 2021 Set 1 — Question 33
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Communications → Information Theory → AWGN Channel Capacity
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Question
A speech signal, band limited to , is sampled at times the Nyquist rate. The speech samples, assumed to be statistically independent and uniformly distributed in the range to , are subsequently quantized in an -bit uniform quantizer and then transmitted over a voice-grade AWGN telephone channel. If the ratio of transmitted signal power to channel noise power is , the minimum channel bandwidth required to ensure reliable transmission of the signal with arbitrarily small probability of transmission error (rounded off to two decimal places) is ________ .
Correct answer
9.24 to 9.28
Solution
1.Calculate the sampling frequency ():
The signal bandwidth .The Nyquist rate .
The sampling rate .
2.Calculate the bit rate ():
The number of bits per sample ..
3.Calculate the Signal-to-Noise Ratio ():
Given ..
4.Apply Shannon's Capacity Formula:
For reliable transmission, the channel capacity must be at least equal to the bit rate ..Rounding to two decimal places, the minimum bandwidth is .
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