As bandwidth approaches infinity,the channel capacity becomes?
Answers
The channel capacity becomes 0
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Answer:
The correct answer to the given question is:
As bandwidth approaches infinity, the channel capacity becomes 1.44 S/N0 bps.
Explanation:
When the pace of communication is kept below a maximum that is constant for a channel, Shannon's Noisy-Channel Coding Theorem asserts that it is feasible to communicate over a noisy channel with an arbitrarily tiny possibility of error.
The Shannon-Hartley theorem states that a channel's capacity C can be computed as
C=Blog2(1+SN)
when it has a bandwidth B and a signal-to-noise ratio S/N.
In this case,
if B, the capacity does not become infinite since as the bandwidth increases, so does the noise power.
The Shannon-Hartley law becomes C=Blog2(1+SN0B)
=SN0(NoBS)log2(1+SN0B)
if the noise power spectral density is N0/2 and the overall noise power is N=N0B. (N0BS).
Now\slimx→0(1+x)1/x=e
As a result, it changes to
C=limBC=SN0log2e=1.44SN0,
indicating that the channel capacity is now limited rather than unlimited.
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