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what is the maximum data rate (in bits/sec) of a noisy channel with bandwidth of 2khz and signal-to-noise ratio of 7 (i.e., s/n

User Crag
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To calculate the maximum data rate of a noisy channel, we can use the Shannon Capacity formula, which is given by:

C = B * log2(1 + S/N)

Where:
C is the channel capacity (maximum data rate),
B is the bandwidth of the channel, and
S/N is the signal-to-noise ratio.

In this case, the bandwidth is given as 2 kHz, and the signal-to-noise ratio is 7.

Plugging these values into the formula, we have:

C = 2000 Hz * log2(1 + 7)

Calculating the logarithm:

C = 2000 Hz * log2(8)

Using the logarithmic property that log2(8) = log2(2^3) = 3:

C = 2000 Hz * 3

C = 6000 bits/sec

Therefore, the maximum data rate of the noisy channel with a bandwidth of 2 kHz and a signal-to-noise ratio of 7 is 6000 bits/sec.
User Maxim Fedotov
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