oops forgot to mention something, notice since it's signal-to-noise ratio, not just noise power, we can get more data through by increasing the power of our signal.
Hence the problem with "56kbps": the amount of power you're allowed to put through is limited by the FCC, and so is the capacity - so we only get 40-something kbps..
BTW there are lots of posts talking about the capacity theorem in more detail, for those interested in the maths.
no, "binary" is having only two values, "digital" is having only _a finite number_ of values. in any case talking about it like this is an oversimplification, and it's kinda pointless..
Just wanted to make one thing clear about the relationship between bandwidth (as in the width of radio frequency bands), and bandwidth (the amount of data we can put through a channel). I don't think that this is what the original question was about, but it's in many ways more important, and I thought this might help clear it up for some readers...
The first (the original meaning) of bandwidth is simply the range of frequencies that we're talking about - for example, the bandwidth of a telephone line is fixed at about 4kHz, spanning from about say 100Hz (?) up to approx 4kHz. This is the thing that most of the posts have been talking about. How then did we get first 300, then 1200, then 2400, up to 56kbps (well, 40kbps) through the phone line, when the bandwidth hasn't ever increased?
Well, the second meaning of bandwidth, the one us net users are always complaining we don't have enough of, isn't actually really to do with frequency ranges, instead it just means how much information we can put through the "real" bandwidth we have. Obviously if we have more "real" bandwidth we can get more "data" bandwidth out of it (eg. if I have 2 phone lines I can do twice as much data (bad explanation, sorry)), but that's not the only way we can get more.
So how much "data" BW can we get out of "real" BW? This is governed by something called Shannon's Law, and it turns out that the key factor is the signal-to-noise ratio (SNR). To get a feel for how this works, imagine that you and I are talking at a really noisy party, so noisy we can hardly hear each other. Obviously we're going to have to go pretty slowly, repeat lots of words ('mmnrnrg!' 'what?' 'mnngvr mgnd!' 'WHAT!?' 'I said, NEVER MIND'), and we're going to be able to get a lot less data through our channel (even though the audio bandwidth is no different) to if we were chatting outside.
Now if you're asking, how much data can we get through the atmosphere, it comes down to how much radio frequency BW there is, secondly how much noise there is, and thirdly how good we are at getting towards the limits of Shannon's law. It's this last one that we've been improving with the successive generations of phone modems, and we're getting pretty close now (when it's worth the cost to do so, anyway), hence don't expect 115kbps analogue modems to appear anytime soon.
BTW IMHO the limits for upper frequencies we can use aren't just to do with electromagnetic propagation, but also to do with our ability to design circuits that will work - now that we're well into GHz & THz we're starting to really feel some of the physical limits (eg. things like electron & hole mobility in semiconductors (which governs how quickly our transistors work & so the upper frequencies they'll work at)).
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oops forgot to mention something, notice since it's signal-to-noise ratio, not just noise power, we can get more data through by increasing the power of our signal.
Hence the problem with "56kbps": the amount of power you're allowed to put through is limited by the FCC, and so is the capacity - so we only get 40-something kbps..
BTW there are lots of posts talking about the capacity theorem in more detail, for those interested in the maths.
Will Bryant, Core Development
no, "binary" is having only two values, "digital" is having only _a finite number_ of values. in any case talking about it like this is an oversimplification, and it's kinda pointless..
Will Bryant, Core Development
Just wanted to make one thing clear about the relationship between bandwidth (as in the width of radio frequency bands), and bandwidth (the amount of data we can put through a channel). I don't think that this is what the original question was about, but it's in many ways more important, and I thought this might help clear it up for some readers...
The first (the original meaning) of bandwidth is simply the range of frequencies that we're talking about - for example, the bandwidth of a telephone line is fixed at about 4kHz, spanning from about say 100Hz (?) up to approx 4kHz. This is the thing that most of the posts have been talking about. How then did we get first 300, then 1200, then 2400, up to 56kbps (well, 40kbps) through the phone line, when the bandwidth hasn't ever increased?
Well, the second meaning of bandwidth, the one us net users are always complaining we don't have enough of, isn't actually really to do with frequency ranges, instead it just means how much information we can put through the "real" bandwidth we have. Obviously if we have more "real" bandwidth we can get more "data" bandwidth out of it (eg. if I have 2 phone lines I can do twice as much data (bad explanation, sorry)), but that's not the only way we can get more.
So how much "data" BW can we get out of "real" BW? This is governed by something called Shannon's Law, and it turns out that the key factor is the signal-to-noise ratio (SNR). To get a feel for how this works, imagine that you and I are talking at a really noisy party, so noisy we can hardly hear each other. Obviously we're going to have to go pretty slowly, repeat lots of words ('mmnrnrg!' 'what?' 'mnngvr mgnd!' 'WHAT!?' 'I said, NEVER MIND'), and we're going to be able to get a lot less data through our channel (even though the audio bandwidth is no different) to if we were chatting outside.
Now if you're asking, how much data can we get through the atmosphere, it comes down to how much radio frequency BW there is, secondly how much noise there is, and thirdly how good we are at getting towards the limits of Shannon's law. It's this last one that we've been improving with the successive generations of phone modems, and we're getting pretty close now (when it's worth the cost to do so, anyway), hence don't expect 115kbps analogue modems to appear anytime soon.
BTW IMHO the limits for upper frequencies we can use aren't just to do with electromagnetic propagation, but also to do with our ability to design circuits that will work - now that we're well into GHz & THz we're starting to really feel some of the physical limits (eg. things like electron & hole mobility in semiconductors (which governs how quickly our transistors work & so the upper frequencies they'll work at)).
Will Bryant, Core Development