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  • I'm gonna talk about bandwidth on, actually, just to be really old fashioned about this.

  • It's 60 symbols video, and it's got a symbol, which would be Delta F.

  • Because it's a range of frequencies, it is related to the amount of information you can get down the fiber.

  • So you know the band width of your broadband is telling you how much information you actually getting there is largely limited by how much you're prepared to pay your broadband company.

  • But there's a sort of fundamental physics limit as to how much information you can actually get down safe.

  • A piece of fibre optic cable.

  • You can apply this concept to anything to sounds to radio waves to light down optical fiber whatever you like.

  • But the idea is the same, which is that essentially light sound.

  • Whatever comes in waves on the classic sound wave or light wave is a sine wave, a little app here, which will produce a total.

  • There we go, here we go.

  • That's a sign wave, and there's no information content in there at all, right?

  • You can't use that to actually transmit information if you actually want to convey information in particular you want to confide digital information you need ones and zeros on that essentially means you need pulses.

  • You can't do it with just a sine wave like that.

  • You need a little, you know, a beep.

  • Then nothing that beep that nothing you need.

  • You need to break it up into pulses, and you can't do that with a single frequency.

  • There's a single frequency.

  • Always sounds like that.

  • It's just a single tone professor.

  • Couldn't you turn it on and off?

  • I could turn it on and off, but actually, then he wouldn't be a single frequency anymore.

  • Let's back up a little bit.

  • Okay, let's do something a little bit more sophisticated, which is So there was my tone and I've got Brady's.

  • I found my phone is June to produce a tone off kilohertz 1000 Hertz and I've set Brady's up to produce a tone off 1001 hurts.

  • Okay, so you know we can play Brady's That's what 1000 1 who it sounds like.

  • And that's and that's what 1000 sounds look really very similar.

  • Very much to tell between them.

  • The interesting thing the hams is if we play them both at once.

  • And if you listen carefully, you can hear that this is strange beating effect that it sometimes louder, sometimes quiet.

  • One way might might make it clear is, if I change the frequency of it, you'll hear that the bee change that.

  • If I take Brady's phone from 1000 1 hurts 1002 you hear that the beats get quicker, so let's turn off the annoying noises for a moment.

  • So physically, what's happening is you got these two ways of slightly different frequencies, and that means they're just kind of overtime drifting in and out of phase with each other.

  • And when they're in phase, the waves, all that up when you get allowed to sound them, when they're out of phase two, the waves cancel each other out, and then it goes quiet again.

  • So you get these beats of loud and quiet, and what I really want is I just want one of those beets.

  • I don't wanna hold your resolve.

  • I want to kind of 11 blip on.

  • I can't quite do that with only two frequencies where I've got only got two frequencies here.

  • But if I had lots of frequencies.

  • Then, actually, I can produce a single beep, a single blip.

  • That's not good, because then basically everything a group you know, adds up in coherently at one point.

  • So you end up with lots of sound there, but then it destructively interferes everywhere else so I can produce a single little pulse of beep on.

  • That's really what I want to do.

  • If I got to convey information digitally, I want to send a whole string of these beeps.

  • But in order to do that, I needed to combine different frequencies together, right?

  • It wasn't just one frequency, it was a whole range of frequencies.

  • And this is very simple relationship between the range of frequencies I add up and how short the beepers.

  • And essentially, it's only write this one down.

  • So essentially, if I've got a range of frequencies Delta F on, I'll produce pulses duration delta t.

  • So the bit the bleeps end up producing the product of the two always comes out to be approximately one.

  • So you see, if I want Thio produce very short pulses if I want to produce it, you know, if I want to pack a lot of information in a finite period of time.

  • I want to use very short pulses.

  • I can put produce, you know, a whole lot of code in a very short period of time.

  • You can see from this former if I want Delta T to be small on the product of Delta F in Delta, T has to be one.

  • As this term gets smaller, the only way I could do that is by making this term bigger.

  • In other words, to make shorter and shorter pulses of sound or light or whatever it is, I need a wider and wider range of frequencies to do it on.

  • The fundamental limits to putting information down a fiber optic cable is what range of frequencies can I put down Because low fiber optic cable, you know, I'll probably let Blue Light go through a red light go through it won't let X ray through radio waves through.

  • It's just no optical fibers don't work that way.

  • And so there's a finite range of frequencies, a bandwidth of lights that I can put down the fiberoptic tape cable on that fundamentally limits.

  • How short a beep I can send down how short a blip of light I can send down on.

  • That's what limits the amount of information you can put down the fiber optic cable.

  • So, professor, when I'm using the Internet and I get a one, is that what's happening to create the one?

  • They're interfering all these different colors of light except a certain one.

  • So if someone that if some of the path between you and whatever server is that you got that one form is down a fiber optic cable, that's exactly what's happening.

  • A little blip of light has been sent down that fiber optic cable to represent the one, and to produce a little blip of light, you need a whole range of frequencies of light to do it.

  • It's not just a single color that can't just switch something on and off, but okay, so that's the weird thing, right?

  • Even if you've got supposing so, everyone thinks like a laser produces light of a single color, single wavelength single frequency.

  • Actually, that's only true if you leave it on forever.

  • If you leave it on forever.

  • So you're not switching, then you do indeed have a sine wave that goes on forever on that is indeed strictly a single frequency.

  • As soon as you switch it on and off over some finite period, it's no longer a single frequency, so even a laser.

  • So again, maybe a picture will help with this, right?

  • If I've got my light, my light wave that goes on and on forever, that really is.

  • If I were a competent of drawing a single frequency, a single wavelength of light.

  • If, however, I just switch it on for a little while, So it's off.

  • Then I got a pulse of light, and then it's off again.

  • This no longer has a single wavelength associated with.

  • It looks like it, cause you can see what it's going up.

  • It's going down, but actually to produce something like this.

  • This is clearly different from this, and to go from having a really single wave to having this, I've got to add a whole want your waves together of slightly different frequencies to produce something like this.

  • And so this is actually the superposition of a whole bunch of slightly different frequencies, even a laser, which you think overs while it's a single wavelength of light.

  • If you switch it on and switch it off again.

  • You've actually produced a pulse of light that has by its nature to contain more than one frequency.

  • If I have a laser, I could just put you on and off.

  • I don't have to do anything clever.

  • I'm not saying I'm producing a little bit of this red light and then this little bit that's a bit bluer.

  • And this little bit it's a bit redder in order to make a pulse.

  • What nature does all that for you, that actually, by switching on and off the laser instead of producing this single for wavelength of light, he's actually producing the right superposition of wavelengths of light to make a pulse.

  • So they're on a bunch of engineers and experts that had to come up with a way to make all these things interfering.

  • Know it all.

  • Don't you know that nature that takes care of it, that just by switching the thing on and off of the right wavelength, the frequency you want to switch things on?

  • The fact that the producing pulses that by its nature produces light which is no longer a single waving.

  • But it turns out that actually this Ah quantum mechanical application of all this as well.

  • One of the things that people know about quantum mechanics is this wonderful thing called the uncertainty principle that says there are various things that you can't measure at the same time, so you can't measure the position of a particle and its momentum at the same time.

  • And one of the other forms of the uncertainty principle is that you can't measure the time when something arrives and its energy at exactly the same time.

  • So if you measure the energy of something and the time of arrival, then that's an answer you can.

  • You can trade them off against each other.

  • You can measure times very accurately, and then you get rubbish measurement of energy and vice versa.

  • And turns out this is a simple example of exactly that.

  • And the reason is we go back to this equation again for a second, that the frequency here, instead of thinking in terms of these pulses of light and the classical picture of waves, think about photons and when a photon arrives, if we've got a pulse of light like that, we know that the light has to arrive sometime within this time, So the photo on we detect is going to arrive within some finite time or other.

  • So because of this relationship up here, because it's some finite time of arrival, that means there's also a finite range of frequencies that that photo on can have, what frequency that we actually measure for the photo.

  • And in terms of frequencies of light.

  • There's a very simple formula that says that the energy of a photo on is related to its frequency.

  • By this relation planks law that the energy of the photo on his planks, constant times, the frequency of the light so on uncertainty in the frequency of the light then translates into an uncertainty in the energy of the photo.

  • We have this trade off right.

  • We can either measure the energy of the photo on arrival very accurately.

  • But because of this uncertainty relation, that means that we can't predict exactly when it's going to arrive.

  • So we don't know what type of time of arrival will be, or, alternatively, we can very tightly force a vote on to arrive at a particular time by saying, Well, we'll switch the laser on off very quickly, which means we know exactly when the photo took off, which means we know exactly when it's going to arrive, so we know when it's gonna arrive.

  • But because it was in the very short pulse, that means is a very large range of frequencies in that pulse, which means the energy record for the photo on is very large.

  • And so there's this trade off this uncertainty relation that says that that you can't measure these two properties of a photo on or indeed any particle simultaneously.

  • You can't measure both its energy and its time of arrival very accurately, the ultimate limit for how much information you can squeeze down.

  • If I rock, the cable is set by exactly this because you might think, Well, you know, I could just keep pushing my partner if I want to pack more information down while I just make My pulse is shorter, and I contend them through quicker that way.

  • But actually, as each time you make the pole shorter, the range of frequencies of the light in that pulse get wider, and eventually you're gonna reach a point where that some of those frequencies of the kind of light that won't go down the fiberoptic cable anymore.

  • So this really is from an engineering point of view.

  • This is the fundamental limits.

  • How much information you could squeeze down.

  • A piece of fiber optic cable is set by this relationship.

  • And what is the limit?

  • What's the shortest post?

  • Uh, I have to look it up.

  • Actually, I thought the calculation.

  • If you want to know, I can tell you, Ah, which lecture that one?

  • Maybe it's a few fender second, few times 10 to the minus 15.

  • So this means for if you've got a fiberoptic cable that just works in the optical part of the spectrum.

  • So just in terms of rough numbers that works from kind of blue light to red light, it turns out that the shortest pulse you can send down that is about offender second.

  • So that's 10 to 0 point 50 14 zeroes, 1 10 to minus 15.

  • So that's the shortest pulse that you can actually send down.

  • That and that that pulse actually contains light.

  • Away from the red did the blue end of the spectrum.

  • If you try and make your pulse and any smaller range of frequencies will push you out of the optical part of the spectrum so you could get zero is where you're going for a one.

  • So you could I mean, you basically your pulse would fall apart.

  • You can't make a nice and the pulse anymore, because you send me some of the frequencies you need to make.

  • That very neat pulse won't actually travel down the fiber.

  • It'll get horribly messed up in terms off data transfer that.

  • Basically, I think it works out.

  • You could send The ultimate limit is you could send about a terabyte of data down a fiber like that in a few hundreds of a second.

I'm gonna talk about bandwidth on, actually, just to be really old fashioned about this.

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最大帶寬是多少?- 60個符號 (What is the maximum Bandwidth? - Sixty Symbols)

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    林宜悉 發佈於 2021 年 01 月 14 日
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