Final answer:
To find the highest transmission rate for a communication channel with a bandwidth of 4 kHz and SNR of 15, the Shannon-Hartley theorem is used. The calculated rate is 16 kbps, and the closest option provided is 15 kbps.
Step-by-step explanation:
The question asks for the highest transmission rate that a communication channel disturbed by additive white Gaussian noise can support given a bandwidth of 4 kHz and an SNR (Signal to Noise Ratio) of 15. To calculate the maximum data rate for a noisy channel, we use the Shannon-Hartley theorem, which states that the capacity C in bits per second (bps) of such a channel is C = B log2(1 + SNR), where B is the bandwidth in hertz and SNR is the signal-to-noise ratio.
Given B = 4000 Hz and SNR = 15, we compute the capacity as follows:
C = 4000 × log2(1 + 15) = 4000 × log2(16)
C = 4000 × 4 = 16000 bps or 16 kbps
Among the options provided:
- a) 60 kbps
- b) 45 kbps
- c) 30 kbps
- d) 15 kbps
The closest option to the calculated capacity is 15 kbps (option d).