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.