Nyquist - the amazing 1928 BREAKTHROUGH which showed every communication channel has a capacity
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- Опубликовано: 1 июн 2024
- In 1928, Harry Nyquist published a paper which would change the course of history [1]. But his original contribution was not the sampling theorem.
Inspired by the work of Fourier, Nyquist discovered that there is a maximum rate at which signals could be sent through a bandlimited channel. For a bandwidth of B, 2B signals per second is the limit (the capacity). This, of course, does not set the limit on how much information you can squeeze into a single symbol/signal, but it shows something remarkable - the bandwidth of the channel limits the signaling rate of a channel. 20 years later, and inspired by Nyquist, Claude Shannon would publish his Mathematical Theory of Communication [2], which combined Nyquist's signalling rate capacity in a bandlimited channel with the impact of noise.
Sources:
[1] H. Nyquist, "Certain Topics in Telegraph Transmission Theory," in Transactions of the American Institute of Electrical Engineers, vol. 47, no. 2, pp. 617-644, April 1928, doi: 10.1109/T-AIEE.1928.5055024.
[2] C. E. Shannon, "A mathematical theory of communication," in The Bell System Technical Journal, vol. 27, no. 3, pp. 379-423, July 1948, doi: 10.1002/j.1538-7305.1948.tb01338.x. 
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Are there are any other historical figures in communication/electrical engineering I should do a video on?
Yes, sure.of course there are a lot of historical figures. Maxwell for example. He's equations is the cornerstone. John Strutt, 3rd Baron Rayleigh, And a little bit courious case with Jocelyn Bell Burnell.
Claude Shannon, develoer of digital communication theory.
Hedy Lamar
Charles Proteus Steinmetz
Check out the biography of Oliver Heaviside by Basil Mahon.
The Nyquist sampling theorem is essentially about trigonometric interpolation, and the relevant mathematical results were known for at least a hundred years before Nyquist. What was not appreciated was the connection of trigonometric interpolation with electronic communication.
Yes. Since you need at least 3 points to determine a particular circle, you need more than two samples (points) to unambiguously determine a sinewave.
@@gnormhurst That's an interesting insight, I hadn't thought about the commonality between geometry and time domain waves. You also have to define a certain bandwidth in order to represent any analog signal with samples.
@@gnormhurstTook me 25 years of trying to understand why digital (audio) sampling works to come to that very insight. That plus really understanding the concept of every waveform being sine-wave intereference. The key thing most simple(beginner) explanations don’t mention clearly enough is you don’t need 2 sample points. You need 3.
Please cite a reference.
Our cellular communications world is the best example of "to the user, technology, when sufficiently advanced, is indistinguishable from magic". Excellent video BTW!
Engineering does not collide with mathematics. Engineering is applied mathematics and applied physics.
Exactly. Electrical (Electronics and Communications Engineer here) I have always said that engineering was applied science and applied mathematics. Cannot be a good engineer without knowledge and love of both
And all are applied Chemistry.
The Creator's Universe is one big Chemistry set: you and me included, Thanks Be!
To Him The Glory!
@@johnfranchina84 yes. And of Chemistry!
@@johncourtneidgeI guess it’s time for a god is an engineer joke.
There were 3 engineers, a mechanical, a chemical and an electrical, having a drink together when the discussion turned to the design of the human body. The mechanical marveled about the skeletal structure, how it was made up as a system of levers with the bones clearly designed to handle the stresses involved. “God must be a mechanical engineer”.
The chemical disagreed. Consider the digestive system, how blood carries energy throughout the body all controlled by the hormonal system. “Obviously god is a chemical engineer.”
The electrical disagreed, “you’re both wrong, it’s obviously that god is a civil engineer”. The other two looked at him, “why do you think that?”
The electrical replied, “who else would put an amusement park right next to a waste disposal site?”
@@johncourtneidgeChemistry is just applied physics.
It's a good think that a few really smart cookies come along from time to time! A really interesting video. Thanks!
Fantastic presentation about some truly special people.
As most signals do are not periodic (even periodic ones must start and end some day and are not strictly periodic but we can ignore the high frequency transients at the start and end) we can not use Fourier series, we use a generalization of them: the Fourier transform where we have a continuum of frequencies and not only the harmonics, basically the um turns into an integral.
This is why Nyquist approach uses samples, but it is a natural way of thinking (as you say accidental) as in practice you can't really go to an infinite resolution.
Apart from that a very nice video.
This duality is brought by Fourier transforms (and more generally by all integral transforms) in many places not only in communication: in Quantum Mechanics for instance you can pass from position to momentum by a simple Fourier transform what leads directly to Heisenberg principle. This is the power of abstract algebraic structures: a simple unifying way to treat several at first apparently unrelated things. Summarizing: several ways to see the same process and a unified way to see several different processes.
That's not how "Fourier" is pronounced
Neither is Nyquist.
@rolandjohansson7428 True, but at least that is how we commonly Anglicise "Nyquist". But his pronunciation of "Fourier" is totally bizarre.
That's why you have to transforme it .
@@davidbroadfoot1864 For real! 😃
Nice. Really like the style, animations, and way of connecting the history.
Well made video! I really enjoyed it. Hope your channel gets more attention and that there will be more videos following. Keep up the good work. Thanks!
Thank you so much for supporting the channel!
Surreal to be glued to my screen the whole video and then see
Apart, perhaps, from the pronunciation of the name Fourier.
“It is difficult to understate the importance of electrical telegraphy…” I think you mean difficult to overstate…
Author of this video should look up how Fourier is pronounced. Fourier was French.
ruclips.net/video/ezkLicWqL4o/видео.html
8:00 - Nyquist criteria. Claude Shannon shows that if you include signal to noise factor, you can really pack more data. In early modems the data signal could still be transmitted successfully, even if it was deeply buried in the noise. As modems got faster, constellation techniques got more complicated. The last old fashion telephone line modems were rated for 33K/56Kbaud. The 56K rate was only possible on a really noise free line, while 33K was a more realistic number. Old American analog telephone lines have a band from 300Hz to 3400Hz, and when digitally sampled, an 8000s/s rate was usually the minimum rate to meet the Nyquist criteria, when practical filtering is included.
I’ve never heard Fourier pronounced the way it is in this video. Anyone else?
My 1.3km telephone line (BT) twisted pair with joints could manage 30Mbs/s on a good day, using BT's fancy cable modem in 2012. Very crafty technology. Not sure how. Some ADSL features on steroids.
Thank you. Very good video. It is sad that it is underappreciated.
I know you're a computer, but it's Foo-Ree-Ay.
Send that computer to school.
And it's Nyquist, not Nayquist.
Fourier is actually said correctly by the robot.
You are thinking of the american way of saying it.
@@herrbonk3635 Interesting. Do the brits say it that way?
@@ahbushnell1 Not sure, but us swedes, dutch, germans, etc do. Modern french people tend to put a little more stress on the first syllable though.
Love the graphics.
Amazing quality. Congrats!!
Nyquist didn’t include the influence of SNR on a channel … Anyone else remember that? Shannon barely got a mention
And not a word about Kotelnikov. Although he described in 1933 about the capacity of the channel. Kotelnikov V.A. On the transmission capacity of the ether and of cables in electrical communications
1933 was after 1928.
@@xandervk2371 There is no question of the possibility of a complete reconstruction of the original signal using discrete samples in 1928. The theorem was proposed and proved by Vladimir Kotelnikov in 1933 in the work "On the bandwidth of ether and cable in telecommunications". Independently of him, Claude Shannon proved this theorem in 1949 (16 years later).
@@xandervk2371 Kotelnikov has priority over Shannon (16 years). Not Nyquist. Shannon was mentioned in the video.
@@sergeikhoudiakov1914 The video is certainly about Nyquist, not Shannon.
very interesting video he was ahead of his time thanks for your work on this!
I remember in high school deriving sine functions from two points. Our trig and calculus teacher would have us write the names of theorems we were using when we did proofs, and I don't recall learning about nyquist sampling theorem, but I do remember working out these kinds of problems, e.g. find a sine wave, or a parabola, or whatever, that passes through these points. And I think I remember having to do a proof that you need 2x the frequency in samples. At the time, I didn't make the connection to transmission lines. I always related math class to other classes at school, or to physical objects, so to me at the time a sine wave was just a wheel spinning or something like that. As an adult, I have encountered the nyquist theorem working on analog transmission networks. For a little while I was working on digital video over satellite/radio -- and some radio heads are all about transmission theory.
although maybe my memory is just off about learning this idea in school. 20 years ago, enough time to forget. haha.
Love you used polar notation at ~ 05:40 background graph. How fitting...
Wow I learned about nyauist from his sampling theory. Interesting how he saw it from the opposite way.
All the things college professors talk about vaguely dancing right infront of you in the video .... Beautiful work ❤
Beautiful
The original complete inventor of sampling theorem and digitizing analog signals was Russian scientist Koteljnikov which has used much older idea of French mathematician Cauchy, Cauchy has even published a paper on converting analog signal to discrete form. Still, Nyquist deserves credit for practical promotion of the earlier work of others.
had no idea.. standing on shoulders of giants
Fantastic, thanks!👏🏻🙏🏻
Brilliant stuff.thanks
Totally agree!
As a old Electronic Tech I respected the Nyquist limits but got lost when QAM came along. My mind just could not comprehend the capacity increase from 50 Baud to 9600 of a 4k bandwidth channel. Much respect to those who really understand this.
See @8:15. Nyquist only limited how fast you could change the symbol, not how many bits you could send on each symbol. If each symbol has only two possibilities, then that's one bit per symbol. But if you allow intermediate values and have 4 levels instead of two, then you have two bits per symbol. If you create two carriers at 90 degrees (in "quadrature") and have 4 amplitude possibilities for each, then there are 4x4 = 16 possibilities per symbol, which means 4 bits per symbol. This is quadrature amplitude modulation: QAM.
Great video. May I ask you how did you create these nice animations?
Good video but it is short on fundamentals, and difficult for the average personto grasp the contents in one go. Still well worth watching and it is disappointing that it has so few views. Modern communications owe a lot to the work of Nyquest and Claude Shannon.
Although the current digital technology greatly aids many facets of today's life, it at the same time has made humans' minds lazier. People prior to the digital-age were definitely more intelligent, imaginative, and creative.
Bravo 🎉
It should be noted that no one named shaniqua, rastus or anything like it, are in the history of human development of technology.
would love some historic background of the time Nyquist discovered, it must have been very interesting the kind of problems that they tried to resolved :)
Yes, learning from the historical perspective is fascinating and useful if you want a fundamental understanding. I think too much is taken for granted if you approach only from a modern day perspective.
This channel's a bomb. I hope you also do videos on Harold Black's feedback work and also many inventions of Armstrong..
Why are these guys not on the US currency? Get rid of those dusty old corrupt politicians! I can't believe I just drove through Gaylord, Michigan and didn't stop to see the Claude Shannon statue!
¡Very good!
Beautiful need more information for bode plot nyquist plot and control system
Perfecto
does Nyquist theorem still apply to fibre optic communication? or was it only for electrical/copper wire communication?
cool.....2B1Q to you too ( go to wikipedia ) or sf/ami or esf/b8zs for more information
It sure does. This is abound encoding information no matter what the media is.
Now, more than ever, it still applies.
Thank-you.
Sadly I didn't understand any of this.
The map of telegraph lines, however, amply illustrated the centrality, then, of The City of London!
And oceanic telegraph lines is how all of this got applied! It turned out that sending DC pulses over thousands of miles of wire, underwater, wasn't as reliable as a couple hundred miles over land. The "high pass filter" characteristic prevented faster telegraphy speeds from being usable. Nyquist proved how that all worked (or why it didn't) and that simply turning up the voltage wouldn't fix the throughput issue. The implications of Nyquist's work were immediate but the long term impact is still being felt. Foundational work.
Your research and content is excellent, but I would prefer if you dropped the background music.
Engineering and mathematics do not collide. They combine.
I would love to know the history of who first applied autocorrelation and autocovariance to extracting communication signals buried in noise and to astronomy imaging.
I was running WSPR just last night on 160 meters, and FT8 this morning on 2 meters ... Astrophysicist Joe Taylor created those modes, and I'm sure he's written papers referencing those who pioneered signal processing before him ... WSPR is good for a -30 dB SNR and FT8 around -25 dB SNR ... WSPR uses a 2 minute frame for, I can't recall how many data plus ECC bits.
shannon & nyquist theorem is fundamental to analog to digital conversion.
thanks, found channel in the recommendations, an idea for a video, make a fpga controller for SDRAM or any RAM
Perfectly good video making an obscure pioneer's contribution accessible to the masses. And, of course, comments filled with people desperately parsing one another's words in absolutely the worst way plausible merely so they can try to demonstrate to one another and hypothetical onlookers how bright they are. But if they are so transparently driven by the compulsions of meat, with no indication they are aware that's what they are doing, then how bright can they be, _really?_
lol
Thank you Scandinavia and Norway (where his family originated from) for discovering this before someone else did. Who could've imagined there would be a limit to things? At the time he lived they thought a boat could have infinite many passengers. So it was nice to find out that it couldn't.
Foo-rear? Oh, please...
good
Converge, yes, collide……not so much.
Does the narrator say 'singal' several times (instead of signal). Otherwise this is an excellent non-math introduction to Nyquist theory.
Excellent presentation. Only please pronounce Fourier as "Foor ee ey" not "Forea".
One of the fathers of the modern world 😉
The other being Claude Shannon.
Went around the barn three times and never opened the door.
Nyquist theory, as I was taught it in Telephone tech school, is sample, quantize and digitize. In other words, a signal can be sampled at twice it's highest expected frequency, quantized into a number, that number digitized and sent via 1's and 0's to a receiver, then the process is reversed. It was billed to us as a means to maintain signal and eliminate noise... not improve bandwidth. That's why the holy grail was, digital to the set, as we have now with VOIP.
Of course, I may be wrong, it was a long time ago.
Check out the biography of Oliver Heaviside by Basil Mahon.
Morse did not invent the code but Samuel Vail did.
Sadly I can’t be doing with all the ‘noise on sound’. Pity really - it does look very interesting.
"Difficult to understate"?
Its still classical American puritan momentum and focus on more reductionistic mapping codes inside out rather than dwelling on deterministic form and shape that Europe has always dwelled in .
If not for proud heritage of uk ,Europeean coalitions and terminology it would've always been willingness to fund & chase code of life, nature ,waves ,feilds its our idealistic nature
Closed system of 1900s structuralism maximizing all the transitor age, chasing particles ,qauntom physics its the phenotypical mosaic fabric
2:14 I think you mean *overstate* 😊
"Difficult to OVERstate"...
Excellent, informative. Two errors" "difficult to understate" should be "difficult to overstate". Also, Fourier badly mispronounced.
Talked about digital information, shows native Americans putting a blanket over a campfire making smoke signals...the first digital comunications.
You can't push a square wave through a round cable.
It’s gonna pop a 6944.. somewhere
It can be done. Only smaller squares can be pushed through though.
Just need to be careful with any bends in the cable, they can't be too sharp.
@@AerialWaviator you can do as you want to.
@@AerialWaviator an x- class pushes a band width where it wants, so what circle or square knows the sun
About 45 years ago, I was a grad student working on a Fortran assignment on a weekend. The building was pretty empty and I was scratching my head, wondering why the code didn't compile. I saw an older (and better dressed) man walking down the hallway and asked him if he could give me some advice. He quickly held up his hand and said (paraphrased) I can't help you, I used to know all this stuff but I can't clutter up my mind with it now.
I immediately dismissed him as a pompous jerk and went back to solving my problem. Later, I found out he was just about the most famous professor on the staff and had at least seven terms named for him and had received the Turing Award.
I still thought he was a pompous jerk, but admittedly a smart pompous jerk.
This is not correct. The `Sampling Theorem' originated with J M Whittaker in Interpolary Function Theory. Nyquist applied it to Information transmission theory
Bells labs Mathematical Theory of Communication ,Shannon
Opinion: Your floating charts, graphs, highlighted text, flying around at the same time as you are describing concepts and ideas is less effective than someone just reading your script silently, with the visual stuff as a reference. Everything colliding together works against your goal of presenting the material.
Nice video! FYI, Fourier was French. I’ve heard his name pronounced FOO-e-yay.
Morse code was developed by Vail.
And that 'American' code was replaced by international versions, much different from the American.
Morse did invent a signalling system but it was impractical.
Vail also invented the 'Morse key', the switch tapped to send the code.
... I could go on about how Morse stole almost all the ideas he's known for but the list is too long.
I thought Lord Kelvin discovered the pulsing of the galvenometer nearly a century before.
Ørsted made his discovery in 1820. William Thomson was born in 1824.
sounds like chatGTP?
Quite difficult to cram such InTeReStiNg information in under 10 minutes (see what I did there:). But thank you.
5:50 "a series of ten pulses" ?!? No! A series of 1 and 0 pulses!
The "ten signal elements" was a Nyquist reference to one second of communication. (note the text in the video, not the audio at the timemark)
Symbols in Morse Code are represented by a combination of five dots and/or dashes.
The speed at which symbols are send was typically at 2 per symbols second, or 10 signal bursts per second.
Note: both the dash, or dah (--) and dot, or dit (.) where send as active signals, the dah being a longer duration, and the dit being of shorter duration.
Not on/off (1/0) like digital pulses. Off, or silence represents space between symbols.
3:02 there were no digital signals at that time....
That did not prevent them from being considered theoretically.
What do you think telegraphy is, then?
@@somedutchguy7582 bursts of noise?
square wave is digital.
@@ivok9846 you have an extremely narrow definition of 'digital', then.
@@somedutchguy7582 one has poetic freedom to call smoke signals digital, but it's just silly....
digital is when machines convert 1s and 0s to something else, not when humans are doing it...
76k views is far too low for this video.
I have always been told that Fourier is pronounced for-ee-ay ... is this yet another U.S. v British pronunciation thing?
No, it's a US vs. French thing😂
@@MrCretesenesithanks fir saying "no" and for laughing at me... very nice... are you British?
No - he’s just wrong. It’s foo-re-ay for everyone.
@@stevetaylor5290I think that you are correct.
there's a youtube video on "how to pronounce Fourier" by a frenchman Julian Miquel - like americans he stresses the first syllable - and the first syllable is more like "FOO" - many americans pronounce it that way - tho i imagine many use the long-O too
There was a girl in my high school math class who said her grandfather was a famous mathematician. Let's call her Laura for her privacy. Keep in mind, you wouldn't impress another high school student with a claim like that. Many years later while learning digital signal processing in EE school I recalled "Laura" Nyquist's story as it dawned on me who she was talking about. That's when I was impressed. True story, cross my heart.
I don’t get it.
WTF?! Anyone with even a very basic knowledge of this field knows how to pronounce "Fourier".
Hmmm, I've only watched the first two minutes and I've seen at least 3 mistakes.
There were many 'telegraph' systems before Morse stole Joe Henry's work. eg Crooke and Wheatstone's railway signalling.
The 'code' was put together by Alf Vail, not Morse himsaelf.
The code shown is the 'International' code, not the 'American' aka 'Railway' code.
Seeing as most statements made are wrong, should I bother to watch the rest?
Thank you for your comments. This video is not an in-depth history of telegraphy but I did not claim there were no telegraph systems prior to Morse. The statement made is Morse's system - in which he holds the patent - became the standard, not that his was the only or even the first system to emerge. International Morse code was by far the most common worldwide, and for international cables. This fits the context of the video better so I am glad it was international Morse code shown. Besides these points, if there are any specific factual statements not correct, I am very happy to receive the feedback because I do make a lot of mistakes.
@@VisualElectric_Thank you for your input.
You say that when Harry Niquist began his work in 1917 not much was known about the fundamental theory underpinning digital communication, dstortion etc. Oliver Heaviside discovered and published the physics theory and the mathematics of telegraph circuits in the 1880s (sorry, lost access to my references so can't be more exact.) He understood what caused inter-symbol distortion and how to mitigate it - later used without permisssion by Pupin, who made a fortune from it. Along the way he invented (and patented) coaxial cable. BTW his only paying job was as a telegraphist - for which he was sometimes mocked by gentlemen scientists.
So maybe Harry did have a few clues when he started?
great video but that's not how you pronounce Fourier.
That's not how Nyquist is pronounced either.
I understand that you may have problems prnouncing Nyquist, but thetes no excuse yo mispronounce Fourier.
Great video, but for the love of God, it's pronounced FouriEr, (emphasis on the E, not the I)!
Think how much more he could have achieved if he had stayed away from America.
I learned about the Nyquist rate in a course taught by a professor Nyquist (no relation).
Ask a French speaker to give you the correct pronunciation of "Fourier".
im not impressed, it was a new technological field and he was among the people developing it, but this development wasn't very creative but pretty basic and natural. He was just at the right place at the right time. His Nyquist plot is impressive though.
The science came "not from the minds of the American capitalists" WTF? How did that get in here? Were they mathematicians or physicists?
😂
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E
A
2:19 I think perhaps you mean ‘difficult to OVERstate …’
He was Swedish. His name meant Newquist and was pronounced 'nüükvist' (ü as in the German language letter).
Otherwise, excellent presentation. Very engaging and calm. Well done! :)
“Discovered the duality between time and frequency?” Huh? Frequency is simple events per time. I’m not sure what’s meant here, but that statement makes no sense.
"Fuh rear?" Can't you do French words?
That was a Social Studies paper for an 8th grader.
I get tired of the affected accents.
I am cringing every time i hear fe RIA instead of FOO riay
I'm sorry, "smoke signals" is a really dumb analogy. Telegraph wires would have much more along the line of simplicity. Perhaps posting on RUclips might be thought of as primitive.