(3/4) Analysis: Explaining Fourier analysis with a machine

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► Learn more at: www.engineerguy.com/fourier
► Buy the book on Amazon: www.amazon.com/gp/product/0983...
► Buy the posters on Zazzle: www.zazzle.com/engineerguy
► Main videos in the series:
(1/4) Introduction: • (1/4) Intro/History: I...
(2/4) Synthesis: • (2/4) Synthesis: A mac...
(4/4) Operation: • (4/4) Operation: The d...
► Bonus videos:
Books and Posters: • Video
Page-by-Page: • Page-by-Page Guide to ...
Spinning Machine: • Bonus: Watch the machi...
Rocker Arms: • Bonus: Rocker arms: si...
This series on Albert Michelson’s Harmonic Analyzer celebrates a nineteenth century mechanical computer that performed Fourier analysis by using gears, springs and levers to calculate with sines and cosines-an astonishing feat in an age before electronic computers. Check out the series companion book and learn how to get a free PDF of the entire book at www.engineerguy.com/fourier.

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31 май 2024

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Комментарии : 136

@mrchangcooler 8 лет назад

I have great admiration for any man who can design such elegant machines. Fantastic.

@TopAhmed1 4 года назад

I am an Engineer my self, and did a lot related to Fourier analysis yet didn't know about this awesome device ...... thx for sharing

@Smashbloon 9 лет назад

This video is fantastic! The production quality looks like something you would see in a large-budget documentary, maybe even better. Also, the machine you present is stunning. Thank you for spending the time and resources to make this!

@superdau 9 лет назад

It always amazes me what people have done purely mechanical before the appearance of electronics (and even then, quite a lot of that "mechanical magic" was used in recent products, like VCRs). Seeing it applied to do Fourier transformation, really the most important thing in engineering, makes it double amazing.

@Banzybanz 4 года назад

Even an odometer (which are still mechanical in some automobiles) which performs a relatively simple task is fairly complex inside.

@sciencoking 9 лет назад

My brain. I just... Dude.

@engineerguyvideo 9 лет назад

I know, man, I know. It took me, Steve and Bruce two years to figure it all out ... just a lot of stuff in that video . . .

@sciencoking 9 лет назад

***** Thank you for the reply! I understand what it does, but what strikes me is the ingenuity that went into inventing such an elegant piece of mechanics.

@engineerguyvideo 9 лет назад

Dennis W Not a day went by -- and I mean this -- when we didn't marvel at the igenuity of this machine's design.

@imrlyboredful 8 лет назад

+Dennis W It took me a long time and a lot of staring at my lecture notes to understand Fourier Analysis...and I've promptly forgotten it since.

@LeaoDN 2 года назад

The most beautiful sinc() function I ever saw - MATLAB can't beat that elegance.

@leomagat7407 4 месяца назад

I APPRECIATE much the innovation and the ingenuity of the engineers who came before us.

@Chillingworth 9 лет назад

Wow. That is incredible. I seriously am astonished by this machine; I got chills when you synthesized the approximated square wave.

@danwest9900 11 месяцев назад

Thank you for posting this - I had never heard of Albert A. Michelson. He must have been a genius to invent and create such a machine as the harmonic analyzer! Incredible.

@RefluxCitadelRevelations 3 года назад

This is absolutely incredible, well done, man. I'm really really blown away by this marvelous machine.

@Afrotechmods 9 лет назад

This is awesome!

@PilotPlater 9 лет назад

I agree! Afrotechmods I'm one of your patrons by the way, fancy seeing you here! :D

@Afrotechmods 9 лет назад

Andy Plater Small internet eh

@BradTheProducer 9 лет назад

1:40 - Forty seconds of video just taught me what four incredibly frustrating years of high school math could not. Why the HELL could my teachers not get the concept of a cosine across to me or most of my peers?

@shaider1982 6 лет назад

When I was still taking my undergraduate degree in mechanical engineering, we had a subject in machine elements where a four bar mechanism can apporximate a function. I did not know that they actually had a machine that actually added lots of those functions!😀👍

@NathanMeyersIsAwesome 8 лет назад

This is my new favorite mechanical calculator. This thing is beautiful, and amazing. Now I want a scale model of one of these! Thank you for showing the world this amazing device!

@PacosAcademicus 9 лет назад

Thank you so much for these videos. I think I have finally understood Fourier Analysis. What an astonishing machine.

@yeswanthbabud2622 2 года назад

Thank you so much sir. Cannot find enough words. The machine is exquisite, magnificent & well executed. Thanks again.

@rthavi4166 8 лет назад

Bill, thank you for your videos. They truly inspire me and humbly remind me that we indeed stand on the shoulders of giants!

@hikaruyoroi 9 лет назад

You are, by far, the best science guy i'm subscribed to on RU-vid, thanks so much for the hard work.

@x0acake 9 лет назад

These are some REALLY well-made videos man. Truly amazing machine.

@VideyoJunkei 8 лет назад

All those levers moving around...and the pen stays still then rather suddenly moves and stays still again.! I wish you had shown the rockers moving here!

@SteveCrayons 8 лет назад

Believe it or not, the rocker arms don't look any different at all at the sudden drop. They just keep moving in their regular pattern. You wouldn't be able to see anything different/special by just looking at the rocker arms!

@willwhite1987 8 лет назад

You'd see all the moving rocker arms move up (resp. down) together. Definitely a pattern that the human eye/brain will catch.

@jmmahony 3 года назад

I agree, I really wish you had shown the rockers moving for the square wave.

@elvishfiend 9 лет назад

Hi Bill, Great video! It's always great to see old mechanisms coming to life. I'm interested as to why you don't see any of the Gibbs Phenomenon when this is plotted, I was wondering if you could explain why?

@engineerguyvideo 9 лет назад

With some imagination and knowing what you are looking for you can (kinda, maybe) see it. The machine just doesn't have enough sinusoid to resolve these high frequency features ... on a 1000 wheel machine I'm guessing you would see it.

@ross302ci 3 года назад

Maybe the large pivot bar and spring act as a sort of mechanical low-pass filter to the inputs from the smaller springs. Like the higher-frequency ones don't have enough amplitude to make much of a difference in the flatter regions, but probably help around the corners when all of the inputs are changing together?

@dnmph 9 лет назад

This is SO cool! I honestly cannot pretend to understand the math behind this, but it is presented in such a clear and succinct way that I feel like I'm following it anyhow. Brilliant.

@saikiransiripuram8747 3 года назад

I got astonished ...such a wonderful explanation with video...cant say in words❤

@CrucialHunter 9 лет назад

You'r a great speaker and teacher. Thank you for this videos.

@kartikch 6 лет назад

The mechanism is amazing and you sir have explained it very well

@halonothing1 6 лет назад

That's really cool. I actually just happened to have read an article on adding sinusoidal frequencies and how square waves are made up of multiple harmonic sine wave frequencies. Neat that I should come across this video right after.

@sixstation6480 3 года назад

Great work...wave theory, potential and kinetic energy, molecular analysis, cycles in cycles...it all opens up the world of science to young and old minds.

@yetihehe 9 лет назад

FINALLY I've understood fourier analysis after all those years...

@88MauJ 8 лет назад

truly a great piece of engineering! Great Work!

@benhsu42 2 года назад

thank you for making this video, this was very cool stuff

@bobbfwed 9 лет назад

That's really cool. Thought I wanted to see the arms when they were creating the square wave. How all of those cosines add up to a straight line!

@HiAdrian 9 лет назад

That's so cool, thanks a lot for this series!

@cr6925 9 лет назад

Wow! Fantastic stuff. Loving it!

@mafurock33 9 лет назад

Thank you for teaching something totally new to me today!

@UntakenNick 8 лет назад

So this is how the Flintstones invented the radio..

@UntakenNick 8 лет назад

+Ignacio Arbea If I weren't "getting" it I wouldn't have been able to associate it with the radio.

@UntakenNick 8 лет назад

+Ignacio Arbea Fourier transform and series are related to the radio, not this particular machine.

@Dr_Xyzt 8 лет назад

I use a series of sines and cosines to draw camshaft profiles and analyze their harmonics, since it's a preloaded spring and mass system.

@teecee1617 9 лет назад

AWESOME! How did the points get there? and how do you determine their value? I see that you set the first harmonic to its max,and all the others relative to that, to make the squariest square possible.

@naiallen1 6 лет назад

Mano do céu! Mind Blowing!! No words for this video, thank you, sir

@engineerguyvideo 6 лет назад

You are welcome

@mr.v6771 6 лет назад

This is food for my mind for a thousand years!

@swsephy 9 лет назад

This machine is so fascinating. Thank you for making these videos.

@chrisbardolph264 4 года назад

It’s maddening even imagining what types of minds come up with these things.

@slehar 2 месяца назад

Very good stuff!

@oldjd7745 9 лет назад

So, this is how is was done before the FFT! Great video.

@skullthrower8904 Год назад

Beyond amazing 🤯

@Maxwell-jn4te 4 года назад

I've got goose bumps!!!!

@botar99 9 лет назад

This is absolutely fantastic! I wish I could show my friends this but they don't appreciate math as much as I do though :(.

@mr.blackhawk142 2 года назад

@BoTARD, (; This is too much "rocket surgery" for me also! L0L

@ChipGuy 9 лет назад

This is even more awesome, looking at this someone can understand how to make the algorythm work on a computer. I.e. what do to with the wave to transform it into coeffiecients. Cool.

@heXan 7 лет назад

If you don't know how "Fourier transformations and back" work then you have a hard time to understand this video. Wonderfully designed analogue machine! :))

@DrumApe 4 года назад

Fantastic!

@probhakarsarkar2430 6 лет назад

You are awesome, sir!

@Ram-zs4hs 9 лет назад

If you were my physics lecturer, I would have been an Einstein. A big like to you.

@digxx 6 лет назад

Didn't you say in the previous video, that turning the crank varies x? Now at 1:50 you say 2 turns of the crank increases the frequency of the cosine by 1? So what do you really mean? Maybe I didn't get it right, but: We start with a_n=10 (n=1..10) and a_n=0 (n=11..20) This is sth like 10* (cos(x) + ... + cos(10x)) So how does this represent sin(x)/x ??

@johanlaurasia 9 лет назад

Fascinating machine

@dandanlec1996 9 лет назад

You just blew my mind :)

@ViofThesea 9 лет назад

mind blown bro. that machine is rad!!!

@policastrotube 9 лет назад

This Mark Hamill guy should read audiobooks.

@dickJohnsonpeter 2 года назад

I'm kind if dumb so I'm not quite understanding lol. My question is should I consider this machine like a mechanical oscilloscope? I know we're way beyond a simple question like that at this point but I don't know what to think about it besides that it's able to do Fourier transforms which I don't even really understand. It seems to me to be like what we used before we had electronic oscilloscopes though.

@derekkuhl 2 года назад

Mindblowing

@coreyfinch5718 3 года назад

Amazing.

@igoronline 9 лет назад

If you ever wondered how computers (synthesisers) generate electronic music, this is it. The shape of the wave gives it's tone, and notes are generated by varying the wave's frequency.

@akshayrao14 9 лет назад

Amazing!!!

@JorgePetrosino 7 лет назад

Brilliant!!!

@d46512 9 лет назад

One of your best videos, nicely done. Call me spoiled but I feel like the machine doesn't so much do the analysis as make it easier to execute. After entering the input function into the rocker arms, you've got to discretize its sinc output and transcribe this into its rocker arms. Then on the second run you get the approximation. Is this correct?

@jcims 9 лет назад

The 'discretization' could simply be done by running the harmonic analysis plot on calibrated graph paper. So basically step one is to transcribe a half period on to the amplitude bars, step two is to run the crank with some graph paper on the platen, step three is to transcribe the intersections in the graph paper to the amplitude bars and step four would be to confirm the analysis with another plot. If it looks good, measure the location of the amplitude bars to get your coefficients.

@ZenvilleErasmus 7 лет назад

Top notch!

@Yutaro-Yoshii 3 года назад

Wow this machine is so clear in principal, it shouldn't be that difficult to implement DFT code after watching this

@cthree87 9 лет назад

So Good

@pseudonym4893 9 лет назад

What level math is this? The highest I've taken is trig but I didn't finish it, so the only thing about this that I understand is what a cosine wave is. How much more would I have to study to encounter what is shown in the video? It looks really interesting.

@lukejtmulder 9 лет назад

For me in Canada I learned it in my fourth calculus course (second year) but you could get there quicker if you wanted to only learn Fourier Analysis.

@Niosus 9 лет назад

Fourier analysis is quite tricky. Mention it to an engineer and chances are he'll cringe. What he shows in this video is a very simple example. It gets really tricky really fast when you delve into it.

@NiftyFingers 9 лет назад

At the core of it, the whole idea is you can express ANY periodic function as a finite or infinite sum of other orthogonal periodic functions. Even that sentence I didn't like... "a periodic function is just sine waves", that's the easy way to think of it. If you are just starting, "periodic functions are just a bunch of sine waves added together", and go from there.

@JoeJoeTater 9 лет назад

I think it kind of depends on how much of it you want to understand. With a year or two of calculus you can follow the math. Conceptually though, it's just sculpting one function from another. I like to think of it like this: you start with a simple wave and bang out the corners with smaller waves until you've got what you were looking for. In that brute sense, it's not too different from a Taylor series. If you like thinking about things in terms of math, I highly suggest finishing trig and taking calc. They're really neat, and you can get into a surprising amount of colleges/classes/jobs just by being competent with calculus.

@nogtname123 9 лет назад

Keep it up!

@snaprollinpitts 9 лет назад

very cool!!!

@Heliumcool1 8 лет назад

Brings back some very bad memories from uni. I never could decide if I hated Fourier transforms more than Laplace transforms. Brilliant mathematical concept and and an even more brilliant machine to see it in action - it's just my feeble brain couldn't cope.

@MathieuBosi 9 лет назад

Great!!

@rdlaughter 8 лет назад

amazing

@lesbsocal9107 4 года назад

Amazing machine. B4 I retired as an electronics tech we'd use a hi tech oscilloscope to do this kind of thing.

@sandyzhang1852 7 лет назад

You are Geniu!

@ihrbekommtmeinenrichtigennamen 9 лет назад

Magic!

@rogerdatt8861 8 лет назад

This is mind blowing! But more accurate periodic functions could be made by increasing the number of terms to greater than 20.

@Halofan830 8 лет назад

They made an 80 function machine as well.

@xxilluminatixxxx 9 лет назад

1000 likes and 0 dislikes great job! :P

@Guitare_picking 9 лет назад

We don't see Gibbs phenomenon ?

@engineerguyvideo 9 лет назад

No ... the resolution just isn't great enough to see that. You can set hints with some imagination. The wikipedia article on "Gibbs Phenonenon" mentions this in regard to this machine.

@djmips 7 лет назад

I see it at 2:56, the pen dips before it rises.

@StudentofLife2718281 9 лет назад

How can I get such a machine?

@dannymaciejewski 3 года назад

I found one on ebay- I’m gunna bring it to work and solve some problems. My boss at home depo will love me

@eddiemorrone870 5 лет назад

Brilliant! sinc(x)... who knew?

@raghudhara3677 7 лет назад

Even functions are symmetric about the y-axis, not the origin (0:52)

@greg55666 7 лет назад

I don't understand what you're saying, that's exactly what the video says. He says "and even" and the right half of the chart flips about the y-axis, just as you're saying.

@raghudhara3677 7 лет назад

he says the right thing; I am referring to the text that briefly appears at the time I mentioned

@greg55666 7 лет назад

Yeah, I'm just not sure it's wrong. He's labeling the origin--so what? The graph is symmetric around the y-axis. I just don't think the animation is misleading or wrong. But anyway, it's not a big deal.

@jonathansebastianpersaud5864 2 года назад

So am not a math guy so I just want to know what the purpose of these machines

@cybernakulum 9 лет назад

Wasn't it supposed to be released on a week-by-week basis?

@engineerguyvideo 9 лет назад

Yeah, but I DO listen to my viewers .... its better to seem 'em all isn't it?

@cybernakulum 9 лет назад

***** It is! I really love this series, so thanks for posting all of it at once.

@Drizzt1343 9 лет назад

***** I'm so happy, I'm actually taking a test on Fourier analysis this week :D

@Niosus 9 лет назад

***** Thanks a lot! You're doing an amazing job at this. Keep em coming! ;)

@kb7vml 9 лет назад

***** Thanks for releasing all of these at once rather than torturing us with a slow trickle over the coming month! :-)

@greg55666 7 лет назад

This video went a little too fast. I had to watch it a couple times to follow it. (You go from setting the square wave on the rocker arms to the chart with the coefficients to resetting the rocker arms really fast.)

@barcodenosebleed5485 2 года назад

Hmmm. Now I want to build a version with about 10,000 levers and run my guitar through it as an analog to more analog converter. Somehow. I'm thinking servos attached to the input levers and the pen going in and out of a coil. Idk. There's something there...