In the infamous Shannon-Hartley theorem the bandwidth of the channel is measured in Hz (Hertz) but the channel capacity is measured in bps (bits per second). So, either I'm missing something obvious or there's a dimensional mismatch in the equation.. Can somebody please help me understand?
Answer
In the equation:
$$C = B \cdot log_2 (1 + \frac{S}{N})$$
The B represents the bandwidth in Hz, and the log2(1 + S/N) represents the "information density" that you can achieve as a result of the signal to noise ratio. This expression has units of "bits/cycle", but this is rarely stated explicitly, since it's technically a dimensionless quantity. It's basically a measure of how many distinct signalling states (e.g., voltage levels) you can reliably distinguish at the receiver, given the noise level in the channel.
So, if bandwidth has units of Hz, or cycles/second, and the rest has units of bits/cycle, you end up with bits/second.
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