Why bandwidth is measured in bits per second?

问题:

According to the definition of the bandwidth, it is the width of the frequency spectrum. Hence bandwidth should be measured in Hz. But bps, Mbps, kbps have been used as the measurement of bandwidth almost everywhere. What I need to know is, why bps, kbps kind of measurements of data transmission rate are used to measure the bandwidth of a signal.

回答1:

Well, in data communications, bits per second (abbreviated bps or bit/sec) is a common measure of data speed for computer modems and transmission carriers. As the term implies, the speed in bps is equal to the number of bits transmitted or received each second.

It is important to distinguish between bits per second (bps) and bytes per second (Bps). One byte is equal to 8 bits.

回答2:

First place to start is the Spectrum. Here the whole thing, from 0 Hz to Gazillion Hz has been mapped out in highway-like lanes. Just as in a highway, you measure the width of the lane by meters, here too, the width is measured in Hz. This is an analog concept. However note, that Hz, is actually a two dimensional concept, not one. It tells you how many cycles are taking place per time. (Hz -> cycles/time) So Hz is not a linear measure like distance. It is a more complex idea, but we tend to forget the time part and plot it as if it were a scalar.

Then we come to digital communications. Here we have two ways of judging how many bits we can transmit per time. This also has a time dimension. Nyquist gave us the first way of estimating how many bits/time we can transmit given a bandwidth, B Hz. He says it is 2 times B, max. But by taking into account signal levels, a completely independent parameter, the number is actually 2 B log2(M). This Nyquist limit is in terms of bits per second. As you see in this equation the term B in Hz has been converted to bps by merely multiplication with a scalar number, M. So they are really the same thing.

Then we have Shannon, who developed an expression that takes into account the noise in the channel and and came up with C = B log2(1+SNR) irrespective of M. This too is in bits/second.

Both of these are way to represent the frequency measure of a signal, which is Hz, into bits per second. Note that both Hz and bit per second are time related concepts and so nothing strange has happened here. Hz and bps are essentially the same concept and directly related.

Bit efficiency is often given in just bits. (bit efficiency = rate/bandwidth) When you divide rate by bandwidth in Hz, the time units cancel and you are left with just bits. Such as 200 bps/100 Hz -> 2 bps per cycle. But this is often written just as bits.