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A noiseless 4khz channel is sampled at every 1ms, what is the maximum data transfer rate?
According to Nyquist's theorem: noiseless maximum data rate = 2Hlog2V (bits/sec) = 8000*log2V, where H is the bandwidth and V is the number of stages sampled. It should be noted that we are talking about a noise-free channel here, so when the number of sampling stages is large, it can achieve very high rates. Note, however, that noise-free is the ideal state, and this will not be the case in practice. It will be limited by Shannon's theorem.