For instance, I work for the government and in their IT closet I see these big racks that are carrying multiple fiber lines which terminate into this box that says:
Nokia 1665 DMX which is apparently something called a “data multiplexer.”
I did some research but I still don’t quite understand what they do. Are they for combining data, tv, and phone signals together from the ISP?
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I’m going to ignore the fact that you’re in a closet where these multiplexers are present and you don’t know what they are, because, although that’s somewhat troubling, they might be for unimportant systems or you might be someone who needs to enter that space for reasons other than maintaining them.
A multiplexer is indeed a device that is used to, in some sense, combine signals.
It doesn’t really combine them. Instead, what it does is it provides the ability to change which input signal is traveling to the output line at any given time. Let’s say you have four different signals coming into the multiplexer from, maybe, four different phone lines. But you don’t want to run for phone lines through a particular piece of conduit that’s particularly small. You’d rather run only two (I’ll get to why it has to be two in a second). One way you can do this is by installing a multiplexer.
As I said, the multiplexer is a device that switches between its various input lines and, depending on a control signal, spits one of those lines out at its output. You can think of it as literally just a switch where you select which input you want to send to the output. You might think this isn’t super useful in reducing the number of cables that you have to run through the conduit because at first it seems like all the multiplexer does, is allow you to pick which phone line is active, but you can still only have one phone line at a time.
That is technically true, but you can get around it. For example, “plain old telephone service” has a signal bandwidth of about 4,000 hertz. It turns out that, for any signal, you don’t have to watch it all of the time in order to reconstruct all of the frequency content in the signal. There is a result called the Nyquist-Shannon sampling theorem which tells you that if you’re looking at a wave, and you just take a sample at a given interval (that is, instead of trying to track the entire wave, you just only look at the value at any particular time at a regular interval) you will have enough information to uniquely reconstruct that wave as long as you take a sample at more than twice the frequency of the wave.
What this means for your switching is that you can actually combine all four telephone signals if you want to by switching between them so quickly that you’re getting enough samples for each phone line. Since you have four phone lines, each of which has a bandwidth of 4000 hertz, if you can switch between each phone line at a rate of over 32,000 hertz, that means you’ll get a measurement on phone line one, two, three, and four at 32,000/4 = 8,000 hertz each — that’s enough to reconstruct the entire phone signal. If you also have an appropriate device at the other end to identify which sections of the signal correspond to which phone line, and a device to decode the snippets back into intelligible phone traffic, then your multiplexer has just allowed you to put all four phone lines on a single cable.
The reason you need a second cable is that, at the other end, you need a way to identify which phone line is which. Even if you had a device that could separate the signals automatically without needing any information from upstream – which might not even be possible depending on what kind of data is being sent – the device would be unable to figure out which phone line was supposed to go where. The device downstream that can separate those signals (not necessarily automatically, as I pointed out) is called a demultiplexer. It does the same thing as a multiplexer, but in reverse. It takes one signal and sends it to a bunch of different outputs depending on what you tell it to do.
So, you need to run another line between the multiplexer and the demultiplexer so that they can share a control signal. That way, both the multiplexer and the demultiplexer no exactly which signal is which and when the switching is happening. When the multiplexer is outputting line 1, the demultiplexer is receiving a signal that’s also telling it “output this on line 1”. The same thing happens for line two, three, and four. So your four port multiplexer has allowed you to reduce four phone lines into a single cable that transmits the data and another cable that transmits the control signal. That might not be super useful in this example because we’re only talking about reducing four cables down to two, but imagine if you did it with 16 or 32 or 64 phone lines. You could really cut down on the number of cables you had to run.
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