But what is the Fourier Transform? A visual introduction.

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An animated introduction to the Fourier Transform.
Help fund future projects: / 3blue1brown
An equally valuable form of support is to simply share some of the videos.
Special thanks to these supporters: 3b1b.co/fourier-thanks
Learn more about Janestreet: janestreet.com/3b1b
Follow-on video about the uncertainty principle: • The more general uncer...
Interactive made by a viewer inspired by this video:
prajwalsouza.github.io/Experi...
Also, take a look at this Jupyter notebook implementing this idea in a way you can play with:
github.com/thatSaneKid/fourie...
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
Russian: xX-Masik-Xx
Vietnamese: @ngvutuan2811
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Animations largely made using manim, a scrappy open-source python library. github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with RU-vid, if you want to stay posted on new videos, subscribe, and click the bell to receive notifications (if you're into that).
If you are new to this channel and want to see more, a good place to start is this playlist: 3b1b.co/recommended
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Опубликовано:

25 янв 2018

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Комментарии : 9 тыс.

@halihammer 8 месяцев назад

It's crazy how Fourier was able to do this with just a piece of paper and his imagination, while I'm already struggling to follow this masterpiece of a visual explanation

@seanriopel3132 7 месяцев назад

And super computers at your disposal. Most people have little comprehension and appreciation for how important and inspired the giants whose shoulders we all stand upon are. The dedication and sacrifice our ancestors dedicated their entire lives to, is without parallel. The one thing they all had in common is a desire for fundamental truths. They were outcasts whose very existence challenged the staus quo. Just because we avoid conflict just to keep things copesthetic doesn't mean it is the proper path forward.

@ivoryas1696 6 месяцев назад

halihammer Yeah, for some people... "built different" is an _understatement..._

@wfps488 2 месяца назад

The guys bibliography is also insane. Born an orphan, became a mathematician, later traveled with napoleon and become a member of parliament. All while creating the groundwork for a lot of quantum physics. Guy lived one hell of a life.

@123deserted Месяц назад

@@wfps488 WHAT? damn, I feel bad about hating the guy when our professor was not even trying to explain the beauty behind fs and ft, I didn't understand them for shit back then, I wanna blame the prof but idk.

@adamcspanza5986 4 года назад

The amount of clever someone has to be to discover this stuff is insane

@theblinkingbrownie4654 4 года назад

It's not just one person, it's hundreds of amazing people.

@nischalada8108 4 года назад

It’s not so much as to “discover” this stuff, but rather, using models and constructs to simplify the world around them in order to understand what was previously too hard to. These mathematicians were just so eager to see nature unravel in ways that unraveled cool secrets, that everything from calculus to Fourier transforms, etc. were built, rather, out of this curiosity.

@AndersAlsDieAnderen9 3 года назад

The amount of clever someone has to have in order to explain it in such a simple way! At university my (very good and passionate Professor) took more than 1,5 hours!

@NovaWarrior77 3 года назад

I am a newb in the regard of creating math, but I would assume it has more to do with seeing enough relevant constructs and making a small or big leap based on alot of background. By no means do you need to be excessively clever to come up with this stuff, not even have a killer amazing amount of background. I just have come to believe that that's the case.

@aurelia8028 3 года назад

I know rite? Especially in math, physics and chemistry, sometimes I'm just sitting there wondering how on earth people managed to find this or that formula, or realize that there was this connection to that, which makes solving whatever problem 100 times easier. Something I still really don't understand is how astronomers figured out the orbital period, velocity and distance to earth of the different planets just by looking with their _eyes_. I also wonder how on earth Newton actually tested his equations of gravity to find out they were correct.

@cusackprep Год назад

You sir truly deserve an honorary doctorate - just for this video. Your impact to generations of confused engineering and math students will forever ripple through our society.

@aaronlatapi2272 Год назад

I totally agree, as a very young engineer math and physics had been thought in only repetition but not in the actual application and manipulation we can do with them. How we can play and control math is a topic i find really interesting and in which im very new at it.

@nosferato445 Год назад

@@aaronlatapi2272 I taught the Fourier transform 'wrong' for ten years.... until I saw his method. his ability to explain things is ungodly.

@JtotheAKOB Год назад

and physicists

@howmathematicianscreatemat9226 Год назад

@@nosferato445 yes, he has both high IQ, really high empathy and the will to be listening towards others. Fantastic combination 😎

@AK-xw2ie Год назад

Fully agree A extremely gifted teacher

@karmapa_TW Год назад

After 20 years of graduation, I now realize what I was learning back then. Thank you for your production.

@Kingd123asdf 4 месяца назад

same here

@TheCodingTrain 6 лет назад

This video is incredible, thank you!

@3blue1brown 6 лет назад

Thanks Dan!

@shreyanshdarshan3199 6 лет назад

The Coding Train good to see you here!

@pierreandferb 6 лет назад

You're my hero!

@evanbecker6743 6 лет назад

It's Dan!

@ianprado1488 5 лет назад

You are a good guy

@Kevin-cy2dr 3 года назад

If this lecture was delivered in a class you would surely get a standing ovation.

@CaseyAtchison 3 года назад

I'm showing it in my class next week.

@akashchoudhary8162 3 года назад

@@CaseyAtchison Well? What was their reaction?

@CaseyAtchison 3 года назад

@@akashchoudhary8162 More than one told me it's the most real science they've ever seen at their school.

@MrAlRats 3 года назад

@@CaseyAtchison So no standing ovation?

@overtheworl 2 года назад

@@MrAlRats funny haha

@raphaelsbr1899 Год назад

Nobody is ever gonna read this, but i'm literaly mesmerized by the quality and accuracy of teaching this video posseses. It's nuts how well u explain such complicated things

@PhilippeSaner Год назад

I read that.

@raphaelsbr1899 Год назад

@@PhilippeSaner i appreciate bro

@simonhinterseer9974 Год назад

didn't read - just clicked thumbs up

@raphaelsbr1899 Год назад

@@simonhinterseer9974 well done soldier

@George-gq1ut Год назад

Nope, we read it and we agree with you. I have 2 decades of constantly dealing with Fourier, Laplace, Smith chart, I came here for new perspectives. We live a revolution of teaching. Oh boy, I would have love to see this 20y ago.

@zhenzhaotu8090 Год назад

As a math student I cannot believe there is a person can make math concept like this intuitive, amazing !

@Zubzub343 6 лет назад

Oh man, I've been following your videos for a while and learnt everytime some new ideas but here you just touched my heart. I studied Fourier transforms a while ago, had good exam result and got a Master degreee in engineering. But still, I've always felt that I missed the correct intuition of Fourier transform. I did some research on my side after the class and got a way better understanding. But still, I think you just achieved what my professors and myself never manage to do, that is teaching/understanding correctly the underlying principle. I cannot thank you more for these video and this whole channel, and to all professors here trying to give some vague intuitions with bad drawing on the blackboard, please, redirect your students to this video. The next generation of engineers will thank you later.

@3blue1brown 6 лет назад

Thanks for taking the time to write such a nice comment. Hopefully, you continue to learn more, there are quite a few great resources on the internet about Fourier Transforms and such (Better Explained has a pretty good one), and I think you'll find many more interesting perspectives and "aha" moments.

@ibrahim_akalin 6 лет назад

and you just wrote down my feelings in this comment, I'm %100 with you! I've been following people on RU-vid and Twitter that are able to learn and teach in deeper and way more intuitive ways, definitely a better path for lifelong learning. Thank you both!

@daggawagga 6 лет назад

Your comment resonates so much within me. I had never even come close to getting an acceptable intuition about these frequency transforms.

@VaderDarth512 6 лет назад

Your the reason i have an A in Calc AB. You make math so fun and interesting!

@HonneyC 6 лет назад

Zubzub343 I was about to right approximately the same comment ! I’m pursuing mathematical studies but it’s the first time in 5 years that I feel I’m getting a good understanding of the way this formula was contrived ! Really had to see it in motion, thank you for that !

@LordFennel 6 лет назад

I'm a first year physics student in the UK. Talking to friends in higher years, I've learnt to dread Fourier Transforms. They are spoken about in hushed tones like a mass genocide in the recent past. I realise this video probably only just scratched the surface of this topic, but I must say how I feel much better informed than I ever could have been by reading a Wikipedia article or even my textbook. Your videos are unique in the way they build up complex concepts from simple ideas in an intuitive, visual way. They are always a treat and have been a fantastic academic supplement in my first term at university. Thank you so much for all your content, 3B1B.

@paulschmitz1275 6 лет назад

Just wanna echo that spirit. Has been a tremendous help to me to, even though my subject area is economics not pure maths.

@NuxTheDragonSlayer 6 лет назад

Fourth year Physics/Mathematics student here and I've got to say first few times I did fourier transforms it was a nightmare and I really didn't know why I was doing it. But after just a few times I came to realise that they are much easier than people make out and so infinitely useful. So I wouldn't be put off of anything if it mentions that it has fourier transforms in it.

@TAP7a 6 лет назад

Yo dude, I'm in my 4th year at Manchester, hit me up with all the questions you want about undergrad physics. I can certainly remember how intimidating the whole thing is, so I would be honoured to do anything I can to help you along the path (I've just taken exams in GR, QFT [which is *all* Fourier Transforms basically] and Statistical Mechanics [also contains a massive amount of FTs], so hopefully I've picked up a few things you can make use of)

@spiritofnux9105 6 лет назад

Came here to say the same: I studied in France and I too hated Fourier transforms... until I watched this video; I had no idea it was this elegant! Many thanks Mister 3B1B 🙂

@jackkingers 6 лет назад

I would say if you are confident on pure algebra and calculus, don’t worry about it. If you struggle with the concepts of what spaces you are transforming into, just don’t worry about it. That will come with time and experience. Just crack on with the maths. Worked for me, and I’m doing my PhD in spectral decomposition electromagnetism!

@kooljirl161 Год назад

why is it that I spent tens of thousands of dollars on a engineering degree, and yet these videos do a much better job at teaching me what the math actually IS than any of my professors... Keep up the amazing work!

@ronitganguly3318 Год назад

university degrees are basically a business

@ttt69420 Год назад

It's because even someone who has never taken pre-calc can see immediate applications to, say fluid dynamics, with inverse fourier transforms if fluid dynamics is something he/she is into. Those are the people that are likely going to use them in research roles or graduate school. Whereas vast majority won't ever touch them in a typical engineering job. It's like throwing out bait to hook one or two students a year.

@SakiDG Год назад

Yeah, my main problem with my degree so far is they teach the pure math... not what it's for. Showing me equations upon equations does nothing for me without a base explanation of the usage. People say these videos don't touch on a proper university education, but without this video I had zero clue. Now I can actually understand the lectures and the math 😅

@evil-wombat Год назад

I've been an engineer for over ten years (my roommate was the signals junkie and I was the embedded systems dude) and you are the first person to actually make me understand the derivation behind this thing.

@eccentricOrange Год назад

> signals junkie I'm stealing this phrase

@ManjunathMarkal 5 лет назад

After 13 years completing engineering , i understood use of Fourier Transforms. thank you sir.

@theowleyes07 4 года назад

Correct

@AdityaX2703 4 года назад

bas formulae ratt ke aoge toh yahi hoga

@BharCode09 4 года назад

@@AdityaX2703 What are you doing here? You better stick to Bhuvan Bam! Looks like typo in searching. Do you speak to your mom in that mouth? Yakk!

@AdityaX2703 4 года назад

@@BharCode09 and i hate bb and indian youtubers

@jaroslavzaruba2765 4 года назад

Thanks for saying that. Now I don't feel that much as such an idiot. Cheers.

@umair5602 2 года назад

7:07 I just realized the reason it's giving a big spike at the zero frequency. When you move the frequency graph up, you're basically adding in another wave with a frequency of 0. The fourier transform still works

@mahxylim7983 2 года назад

You're right!!

@Zylarlander 2 года назад

Woah, great insight

@victorwilburn8588 2 года назад

Yep, good point, it's the "DC coefficient", as we would call it in the context of the Discrete Cosine Transform (similar in concept to the Fourier transform) that is at the heart of MPEG video compression (though I'm sure that term is used in other contexts as well). As opposed to the "AC coefficients". Borrowing terms from electronics.

@Vancuum 2 года назад

Look into the Dirac delta function. It turns out that the fourier transform of a constant is the aforementioned function. Your realization is more profound than you realize!

@mjolnirswrath23 2 года назад

@@victorwilburn8588 correct you want a pure DC waveform molecular Attenuation Field Density , AC hum " 60 Hz " Thus why in order to activate TRUE NMRFA of molecules you have to use Pure source of DC energy Alternating Current " Hum "contaminates a pure Sine wave frequency.. US War department R&D 1946 Infrasonic Waveform Weapons technology.

@chrisengland5523 Год назад

I remember struggling through the maths of Fourier transforms at university, many decades ago and I've long since forgotten it all, but this video is a very intuitive explanation. I just wish we had had such graphical illustrations when I was trying to understand it.

@mahxylim7983 Год назад

Words cannot convey my gratitude to you with making these videos, you are helping so many people all around the world to see the beauty of math, for what it really is. Thank you. You taught me more than any of my Math teacher ever did.

@p337maB Год назад

This is not only helping many people to see the beauty of math. People who understand these concepts more intuitively become better engineers, physicists, software developers, ... Better teaching creates a better world. I wish there was a 3Blue1Brown for every field

@mahxylim7983 Год назад

@@p337maB Let's contribute to the society in ways we are capable, and eventually more 3B1B will appear. :)

@cagedgandalf3472 Год назад

@@mahxylim7983 That is true

@MrPlasticsnowman 3 года назад

I want to say one thing: Your skill in not only understanding and vocally explaining these concepts is so perfectly complemented by the animations you create that it blows all other resources on this topic out of the water. Even my college professors recommend this video specifically because, and I quote, "I could never create something so masterful that so aptly explains what is going on inside my head." Your skills are a gift to us all! I hope you always find as much passion in creating these videos as I do watching them.

@benjaminknudson5997 2 года назад

It's incredible honestly, 3blue1brown and Sal Khan have made such massive impact; I might need to learn some chaos theory just to try to measure how we have profited as a species from just those 2. I would like to recognize educators in general for their hard work and passion, although, I think we can assess that a few individuals can be attributed a great deal of impact, similarly to say physics. There is a subset of a subset of individuals we can point at who we say have made great contributions, although if you point at them they almost certainly just point somewhere else; a giant standing on giant shoulders perhaps.

@alien9000555 2 года назад

He is doing history

@aussiedog5221 2 года назад

Become a supporter of Grant. I did....after watching his videos for a few years. His math videos are worth a few bucks a month.

@yt.abhibhav 2 года назад

@@benjaminknudson5997 You should include "StatQuest" as well in your list sir

@macronencer 6 лет назад

I think you might be the best communicator on RU-vid. This is a flawlessly clear and concise presentation. I'm so glad you are planning to make a sequel too, and get into some other concepts!

@47Yeoman 6 лет назад

Agree. Agree. Agree.

@Duerschaedel 6 лет назад

totally agree!!

@sanket7402 6 лет назад

Yeah! Agree..

@46pi26 6 лет назад

This should be a template for all comments on RU-vid. It's perfect.

@brewbrewbrewthedeck4138 6 лет назад

Now now, let's not exaggerate.

@asciizero1099 Год назад

This is by far the best, simplest, clearest and nicest explanation on the subject. Thank you so much! You're a hero

@ameymeher4559 Год назад

I almost cried watching this video. Such great explanation! Everyone deserves this

@nyahhbinghi Год назад

it is a thing of beauty

@parkerstroh6586 Год назад

bloody hell me too ahahha

@abc7297 4 года назад

When you understand the main idea of Fourier Transformation finally in a youtube video instead of in a whole semester in university.

@jimjim3979 4 года назад

It's even better sometimes on RU-vid

@orti1283 4 года назад

I can relate to that feeling too, but to be fair, it probably finally sunk in because you had built notions and worked with them before despite not understanding them to this level of intuition

@marcoottina654 3 года назад

this video should be proposed in EVERY FUCKING CLASS

@johnevon8220 3 года назад

@@orti1283 good point

@crl122486 3 года назад

I actually watched this before studying this in uni. For new people, this will shave off about 80 hours haha

@vaibhavtiwari8700 5 лет назад

"chaos and chaos and chaos chaos chaos, and whup things line up pretty nicely" *repeat* -- My life

@GubeTube19 4 года назад

I read this comment exactly at the same time he said it in the video lol

@emilandersenaudio 4 года назад

love the WHUP

@TaborPrzemyslaw 4 года назад

If you think about it, events in life are kind of like different frequencies that sum up

@980616 3 года назад

Good one!!

@thehumbleworldtrotter691 Год назад

If I had had a chance to look at your vdo 30 years back during my electrical engineering classes, I would have fully grasped what I actually completely lost back then. My goodness, your explanation and graphich presentations are unmatched by anyone on this planet.

@Pabloghghgh 2 года назад

I'm struggling a bit with FT-NMR concepts and this has been INCREDIBLY helpful. Can't thank you enough.

@simonblaha 4 года назад

1:50 Seeing a mathematical representation of a Dminor7 chord is all my jazz-mathematician soul ever needed.

@androidiscool7437 3 года назад

♪ D minor 7 with 3 Blue 1 Brown ♪ - D F A C Intensifies

@calyodelphi124 3 года назад

I just came back to this video again after a year or so just to re-watch it because thanks algorithm, and I came down into the comments to make this exact same comment only to find this one. :D

@Alex-ud6zr 3 года назад

I take it you enjoy the Black Saint and the Sinner Lady then?

@calyodelphi124 3 года назад

@@Alex-ud6zr I'm not terribly well-versed in specific jazz artists/bands, unfortunately. I've just had a few years' worth of band experience in high school and subsequent music theory osmosis vis a vis Adam Neely more recently. ^^;

@Alex-ud6zr 3 года назад

@@calyodelphi124 Coolio. Well, if I have but 1 album to recommend, it would be The Black Saint and the Sinner Lady as it 1. fits the description, and 2. across the 2000 albums of which I have listened to and logged, it stands as the most perfect representation of music that I have personally ever had the pleasure of listening to. :>

@Capitalust 5 лет назад

This channel is literally one of the best things that has happened for the mathematics community. Such valuable content.

@adityasanthosh702 5 лет назад

@Piyush Satti Haven't you been seeing other comments which are recent? And 3B1B channel is growing day by day. I just found this channel a few days ago for which i am very thankful

@SuperReddevil23 4 года назад

True, so true, my conceptual understanding of fourier transform has grown exponentially

@LarryMcLarren 4 года назад

I would go as far to say for me, it is the best channel on yt

@rohan1002 4 года назад

I would also recommend mathologer

@Turbomachinsky 8 месяцев назад

Absolutely, positively, the most stellar and intuitive introduction to Fourier transforms I have ever seen. You have far better explained, in just 20 minutes, what my uni lecturer ever could in a semester back in the day.

@ulasozbent9248 Год назад

It is unbelievable that there is such a simple explanation for the "thing" that the teacher has been teaching for months but left undefined! Congrats sir!

@gonzalobera96 6 лет назад

Your videos sir, are a gift to humanity

@berbudy 6 лет назад

so true, I'm so glad this guy exist

@JorgetePanete 6 лет назад

berbudy exists*

@SameerAnsari-yj1tt 6 лет назад

So Trueee...!!!

@IceMetalPunk 6 лет назад

I somehow managed to get a computer science degree without once learning about Fourier transforms (though I narrowly avoided them several times). I'm not sure how I did that. But watching this video, they make complete sense! So often, "complicated" math concepts are taught purely symbolically, but understanding *why* they work, from the ground up, is extremely important -- and, for me, it's the thing that makes math fun! I guarantee I won't remember the details of this in a few months unless I watch multiple times, but if I ever run into a need for Fourier transforms, I also guarantee I'll be thinking of this video to figure out what I need to do :) So thank you :)

@dp0813 6 лет назад

IceMetalPunk Explain it to yourself a few times after watching the video a few times, then explain it to others so they also see the big picture. That is one of the best ways to learn it. 👍😊

@sudoLife 5 месяцев назад

The way you connect the concepts is so amazing! I can't even begin to imagine how much effort you put in your own education.

@50srefugee 2 года назад

My life would likely have been very different if these videos had been available to me when I first attempted calculus fifty years ago. I learned a set of rules for working with equations. But when I hit integral calculus, I had only the dimmest understanding of what those rules MEANT, and found I could go no further. With these videos, I might well have been able to climb over that wall, and see much further from its summit.

@paulbarton4395 Год назад

Even the calc books are better nowadays, bigger with better pictures and more geometrical explanations, nicer formatting (but more $$$ also)...I've seen math texts from 50 years ago, they don't look fun

@aoliveira_ Год назад

@@paulbarton4395 I don't like "fun" books. They look like childish.

@aoliveira_ Год назад

Sometimes is good that the books are difficult. Sometimes you are understanding just because you feel that you are following but in fact you are not understanding at all. Trying to figure out difficult things makes you realize and correct that.

@paulbarton4395 Год назад

@@aoliveira_ I was referring to the books formatting, under the assumption that the content is correct and rigorous. Books from 1950 have tiny, cramped text and bad images. LaTex formatting has improved everything, and as for visuals, our ability to generate 3-dimensional plots can help build intuition.

@polygontower Год назад

@@aoliveira_ Fun in this context means more understandable and intuitive

@mokopa 6 лет назад

I often wish youtube had a better way of indicating HOW MUCH I like a video. This one would have scored high.

@franciscofarias6385 6 лет назад

yeah, by youtube standards i liked this video and the one with the rat taking a shower equally

@briancooke1906 6 лет назад

right! If I click like really hard, it just likes.

@Israelpwn 6 лет назад

About 8 years ago, YT had a 5 star ranking system. I preferred it a whole lot more.. However, that meant you couldn't save the video in a "liked" list unless you favourited it.

@AaronRotenberg 6 лет назад

Mikky They got rid of the five star rating system because the vast majority of ratings were either one star or five stars. People are hesitant to give a "bad" (read: less than five stars) rating to anything that has no significant flaws, even it is fluff rather than solid content.

@SeraphimKnight 6 лет назад

Remember when youtube had star rating for videos? I always like that system better.

@beenaplumber8379 3 года назад

I'm a retired neuroscientist and now a part-time middle school teacher. I teach digital music production, and I rely heavily on Audacity software in my class. The noise reduction algorithm relies on Fourier transforms (which I have never understood adequately), and this video has helped tremendously! Thank you so much! What an intelligent way to reduce unwanted noise! Far better than a simple noise gate. Nice to finally understand the way it works. Sorta...

@ahreurink 3 года назад

Don't you use fourier transform in interpreting EEG in neuro science?

@beenaplumber8379 3 года назад

@@ahreurink In my research, I never used EEG readings. I know they do use a complex noise reduction algorithm, and I'll bet it is the fourier transform. My work involved more of the molecular biology and behavior, and my labs mostly used animal models. Getting an EEG reading on a poor little mouse is not easy.

@MadScientist267 2 года назад

Until you end up with the NR gurgles lol

@LunizIsGlacey 2 года назад

@@ahreurink Wow, neuroscientist to digital music middle school teacher is not a career path I would’ve guessed! Your interests and skills must be very diverse.

@kidzbop38isstraightfire92 2 года назад

They teach digital media production in middle school? That seems so niche lol

@snehadash7117 Год назад

I love how lucid and elegant and visual 3b1b videos are...How each step is derived from the previous one and how we build up to the final result from almost absolute zero through a very intuitive and systematic sequence of steps❤ We are blessed to have this channel Loved every bit of this video's brilliance!

@NandhiniChandramoorthy Год назад

What an elegant explanation! I wish someone had taught me the concept of Fourier transforms with such clarity when I was an engineering undergrad . Leaving aside the excellent visualization for a moment, just this insightful way of looking at fourier transform- winding frequencies and all, makes it understandable finally. You, sir, are truly a genius !

@wwkx 6 лет назад

I'm studying engineering and I've been passing exams like calculus and acoustics where the concept of Fourier Transform (and Laplace too) should be well understood. But nobody ever explained it clearly or tried to, they just gave us the formula for the series and that's it, we basically had to accept it blindly. Researching on my own just gave me back analytical processes to get to the final integral, but without explaining the meaning of each step and just putting even more confusion in my head. I also like to make music so I've been playing around with equalizers and the like for a long time and I ended making up my own idea of how the frequency analysis actually works. But now in just 20 minutes you managed to fill one of the biggest gaps in my knowledge and I'm so happy you made this video, like from 14:29 on I really started seeing rainbows all around lol. Thanks a lot for this vid, I can't wait for the next ones

@emmanueloverrated 6 лет назад

Same experience as yours. I had to accept the transform without understanding what was the thinking process of M. Fourrier. Pretty sure he was teaching it that way, when alive. Upper grades in mathematics would be much more interresting with explanations like these. Professors are lost in the abstractions and have lost (or never had?) the art of transmitting the knowledge.

@Ayplus 6 лет назад

wwwKx same here buddy

@Ayplus 6 лет назад

Truth

@elherediaenc 6 лет назад

Truth has been spoken here! This video is helping me to understand Computational Photography concepts (Processing,etc...)!

@tricanico 6 лет назад

jshowa o maybe it's important to read a little bit of Shakespeare here and understand we are humans After going through that, i believe it's important to understand stuff for the future of humanity, don't you find it odd that math is taught so badly? And that people that studied math a couple hundred years ago not more were chased and burnt to death? Something's going on here. But even more practically: don't you think that when you understand stuff you just are faster and better doing everything?

@willypataponk 6 лет назад

In 20 min you've explained what my Analysis IV teacher failed to do during a year. You're fantastic!

@RedLamentations Год назад

I wish I could express how thankful I am to you in a way that is more than just words. You have continued to provide free, quality content that has helped me to understand so many concepts in my engineering classes, and in most cases you’ve done a better job in an hour than the professors have done in a months worth of classes. From the bottom of my heart, thank you

@danishali8335 Год назад

Brother, You deserve an applause, because of the Explanation and the Modeling of the video. I really appreciate your work, and all of us are thankfull to you, God bless you

@maxithewoowoo 6 лет назад

in case anybody is interested, this acko.net/files/gltalks/toolsforthought/#28 website gives a live demo of the stuff 3Blue1Brown talks about, winding a signal around a circle at different rates and calculating the average. It's a bit CPU intensive so it also converts your computer into a quick heater if you need one :D

@calyodelphi124 6 лет назад

Omg I have to bookmark this link now! :D

@LordDecapo 6 лет назад

Thanks! Great link :D

@aelolul 6 лет назад

Wow!

@MrMineHeads. 6 лет назад

Dot

@mouryapesala 6 лет назад

Dot Dot Dot

@vishnukumar4531 5 лет назад

This video gives me chills . How could a person come up with such elegant explanations 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥

@winterbird4069 2 года назад

I’m into my third year of one of the most prestigious programs at one of the most prestigious universities in my country, and even there they fail to simplify the core concept as well as you do. The visuals and examples you give are 100x more comprehensible than what my profs have tried to explain. Thanks for helping educate the world in a better way :)

@lucasfreitag9794 Год назад

Genius analogy ! I often rewatch your videos to freshen up my intuition. It is so nice to have your animations and ideas to better understand difficult concepts taught in University.

@erikziak1249 6 лет назад

This is one of the highest quality content on RU-vid.

@trottsky87 6 лет назад

I am an electrical engineer and I studied Fourier Transforms in university and remember not understanding how it works. In my job I actually use Fourier Transforms to view the frequency domain, but again tools calculate it for me. When I viewed this video, it was the FIRST time in my life I finally understood how Fourier Transforms work! I absolutely love this video! Awesome job!

@xavierbolivar-hazboun1347 5 месяцев назад

I've been coming back to this video every couple of years as I get through my university career and makes more sense everytime. Cheers!

@AdityaSharma001 2 года назад

I just cannot express how amazing your explanations are, because that praise will still be less. So I just want to thank you a ton for helping us and making a better knowledgeable future.

@MisterMcHaos 6 лет назад

Sometimes - just *sometimes* - one needs access to a "double like" button. Well done, 3B1B.

@Renanbmx123 6 лет назад

I agree my friend !!!!

6 лет назад

In this special “sometimes case” I would be tempted to hit that double button multiple times.

@zbzb-ic1sr 6 лет назад

I wish grant had a video on tensors, been browsing the internet and I can't get an intuitive feel on tensors.

@HattoriHanzo62 6 лет назад

Yep, one per turn :-)

@oafhauohguoihgakds5151 6 лет назад

actually on windows you can do it by pressing alt+f4

@Pear.Jerry. 6 лет назад

I study Applied Mathematics and I think of myself as of someone knowing quite a bit of mathematics and also (from what others say) having some sort of skills in transferring this knowledge in a pretty understandable way to other people. But compared to you... Well - YOU ARE SIMPLY A DIDACTIC GENIUS! The whole 'scenario' of each episode, the way you move from the things which are very easy towards the more difficult ones, the examples that you pick, the interpretations that you find, the visualizations... Each video is just a mathematical masterpiece! Thank God there was a moment in your life when you thought that your mission is to show the people the beauty of maths on RU-vid. I cannot think of anyone doing it as good, as you do. :)

@azursmile 2 года назад

This video really helped me out of a bind where I was expected to understand FT with hardly any intro. Thank you so much!

@101_huzefajohar7 Год назад

I can’t express in words how grateful I am to you for helping me clearly understand and visualise the logic and derivation of such a comlplex mathematical topic. Youre really doing an incredible job! There is no comparison of the quality of third class education given to us in Indian colleges and what amazing content you are giving for free!

@dl0.0lb 6 лет назад

Dang - I stopped taking math in 10th grade after my AP Math teacher took me out of the program because I didn't like doing all the extra homework. After going to school for music but becoming a programmer, I continued to learn more advanced math as needed. I've had random times where I've used the Fourier transform, but never really understood it or why it worked. This made it crystal clear and it feels good to fully understand what is going on both conceptually and in the notation. Thanks a ton for your time putting this together.

@MrxstGrssmnstMttckstPhlNelThot 6 лет назад

Gotta convert numbers to a base with more fours in it. So it's fourier. For example: Take 12057 make it base 9. Which gets 17476. Then 17476 to base 16 is 4444. That number is the fouriest. Good job! ;)

@maitenoda1730 Год назад

I'm stunned by the clarity this video brought me. Thanks so much for puting materials like these in a free platform. Your didatics is amazing. Congratulations!!

@ruaraidhmcdonald-walker9524 5 месяцев назад

Beautifully done. Went looking for a simple way to explain this to younger engineers who can use it but don't "feel it" and you sir have just nailed it. Perfect.

@pranit9668 6 лет назад

Oh.. My.. God This thing just taught me more math that 2 yrs of Engineering lectures couldn't teach me

@johnmichael1594 5 лет назад

taught you MORE than 2yrs of lectures COULDN'T teach you??? what 2 yrs of lectures COULDN'T teach you is almost infinite, so your statement becomes trivial. apparently X yrs of language and composition lectures likewise failed to teach you how to express yourself accurately and precisely. maybe you're just not college material. or maybe you need to learn to think FIRST and only speak afterward, rather than blurting out the first thing that pops into your head.

@adam_nasir 5 лет назад

Dude... perhaps English isn't his first language. There's no need to insult or put someone down online due to a simple grammatical error.

@johnmichael1594 5 лет назад

+Adam Nasir - if you think my comment to pranit was insulting or contained a put down, then YOU are an touchy-feely politically-correct IDIOT. see the difference? THAT is an insult (even tho conditionally true). i corrected a blatant LOGICAL error that had NOTHING to do with the commenter's native language, and everything to do with careless sloppy composition. sloppy speaking (or writing) is the surest barometer of sloppy thinking. also, don't you think pranit can defend himself if he felt the need? aren't YOU the one being condescending by ASSUMING that pranit needs you to butt in and defend his honor? how arrogant and presumptuous, not to mention passively-aggressively insulting to pranit. or are you too "logically challenged" to follow the implications of your post to their inescapable conclusions? dimwit.

@blunderbus2695 5 лет назад

+John Michael gr8 b8 m8

@JoSh-yu6jt 5 лет назад

John Michael You two are having a misunderstanding because judging from the type of answer you both decided to give... a) you made logical approach, focusing on the logic problem of the original post, whereas b) Adam Nasir interpreted pranit pawar's message a different way by guessing its intended meaning and perceived your message probably as quite blunt. Therefore - and this is my perspective and how I interpret the collision of you two - you two may be talking about the same topic but on two different levels. Whether or not this conversation makes sense is a whole different question, because we don't know how pranit actually meant his message to be understood. Was he being sarcastic? Was he having a bad day and he used this message to express his emotional situation? ...which btw isn't more than a tiny snapshot of what pranit really thought when he wrote this. Or are we thinking waaaaay too much about all this, because pranit just wanted to express that this video is genius because it explains a complex topic in so little time? If the topic is important to you it can help to ask the one who gave a statement, how he/she means it. That helps you understanding whether your thoughts are relevant. Or don't ask, speak your mind and prepare for conflict. ;-) Communication is a beast. 🤙🏼^^

@AleksandarBosakov 6 лет назад

15 years ago I was a chemistry student and I had to take exams on linear algebra and calculus. And I specialized in spectroscopy. That was a long time ago, now I'm in another sphere - computers, and I've forgotten a lot of details, though not the basic concepts. Let's just say, your videos made me connect a lot of dots in my mind. Incredible work, man. See, it did happen for me to teach - there was a schoolgirl next door, whom I sometimes helped with the lessons. Once she told me that she gets higher grades if I explain the lesson to her and that I was born for a teacher. Yet it's guys like you, that I take my lessons from.

@teachies902 Год назад

this is awesome!! i've been working on a project involving decomposing waveforms into their harmonics, and these videos clear up so much.

@trenvert123 8 месяцев назад

The way you explain it makes it much more interesting. I went from wanting to know what it is, and not getting a good definition from Wikipedia, to wanting to create one myself. Thanks!

@aryamsthapak7095 4 года назад

"Kind of...This is...a bit of a lie, but it's in the Direction of the truth" -A great mathematician

@hassanakhtar7874 4 года назад

Great teacher*

@hichamsabah31 3 года назад

A sign of wisdom.

@ronzang 6 лет назад

11:50 "..since its a little more complex.." I see what you did there

@eicydee3212 Год назад

These videos are amazing, thank you! Heard about all these topics in lectures while studying, but never really understood them, managed to pass the exams anyway, got my degree and never needed this math again. And these videos make me really understand how these things work and how everything just lines up if one looks at it with the proper mindset. Really a blessing for today's students and everyone who is just interested in it.

@bibekluitel6113 23 дня назад

Loved the way how you explains and how you go deeper in the relevant field.

@Shaparder 3 года назад

Words can't even describe how incredible this video is. It literally made made me tear up of joy. You are the best teacher ever, period.

@TheLoukas77 2 года назад

I am moved too, I just cant believe I finally got intuition for something I'm striving to understand for years in just 20minutes.

@yasminebelghith6741 Год назад

This isn't the way I pictured someone crying because of math

@stkyriakoulisdr 6 лет назад

From Neural Networks to Fourier Transform to Linear Algebra and Calculus... A Like is not enough really for all the work you are doing

@markfisherectuals 5 лет назад

sponsor them on patreon, it'd really help them, and us, in making more of these beautiful videos, more often.

@7gamezone 5 лет назад

SOOO TRUE!!!!!!!!!!!!!!!!!!!

@sahandsoltanieh5186 5 лет назад

I confirm that :)

@orangeheartguy 2 месяца назад

I absolute love how you represent these complex mathematical ideas with such beautiful illustrations. I also appreciate the touch of explaining a concept you know people might be confused by taking time to explain all the components, especially when you were talking about the winding of the signal around a circle. I also appreciate how you break down the formulars by building the understanding of the viewer first then, like building blocks reconcile all that has been taught. I literally search for your channel + the topic name when I want to get a beautiful understanding of mathematical concepts. Thank you for all you do. I'm very sure a lot of college students like me deeply appreciate you. The fire of my love for math burns brighter after your videos. After watching this, I'm definitely going to check if you have one on z- and Laplace transforms.

@juanrossi3 2 месяца назад

I'm speechless with this work of art. The explanation of the underlying principles is amazingly clever, and the visual production is outstanding. I can't imagine the amount of hours needed to make all of this. It's an honor to have watched your video!

@aureusyarara 6 лет назад

wth this was always this easy to understand??? I quit engineering school because I simply couldn't get this (and Z transform) and omg it was needed for EVERYTHING past that one class... Maybe I can consider going back.

@Flerovium 6 лет назад

you can do it! i quit computer engineering class after being a failure at math but after that I have learned so much more about math by educating myself.

@steevepierre-louis9418 6 лет назад

go for it!

@lukapopovic5802 6 лет назад

I habe some reaction watching any video of this guy. If linear algebra was also problem for you I hardly recomend his series (10 or so videos) about linear algebra.

@buh357 2 года назад

Honestly, I watched for around 3 minutes and was already blown away by your explanation. WOW.

@Sunny-qe5el 2 года назад

I had a hard time understanding "Signals and Systems" with Fourier Transform for frequency domain representation of signal. But, everything is so clear now. I am so grateful to have found this video.

@miiortbiiort4610 3 года назад

Funny how we pay loads of money to learn this stuff at university, yet we all still come running to free online video lectures because no professor can match them in terms of quality.

@vapourmile 3 года назад

I was just thinking about how the reason I dislike this kind of RU-vid channel is for the same reason I dislike other similar channels, such as Veritasium, Numberphile, SmarterEveryDay and VSauce. The trouble is, you aren't really learning anything. In University it usually takes a long time and you have to start from the foundations and work your way up through the rungs one by one until you arrive at the point where you can follow what you've learned into the workplace and do it professionally. This kind of channel uses the "wizzbang" or "wow" approach of endlessly cherry picking isolated curios and well known and popular but poorly understood ideas. In University after this you would be tested by having to produce maths or write programs which use what you've learned to show you can. You don't get that here and it's my guess almost nobody who watches this video goes on to actually sit down and write their own FFT. In the end, you just add it to your store of useless information.

@miiortbiiort4610 3 года назад

@@vapourmile Actually, I got to disagree with you on that one. I think you misunderstand the goal these types of channels have in mind. They aren’t academically ‘rigorous’, because such long-winded video’s would only be watched by those already schooled in physics/mathematics. The aim is to help conceptualize idea’s and inspire people to investigate for themselves. The importance of communicating science to the general public is something that’s often overlooked. As for 3B1B, I actually did learn something from this video. My university did nothing to provide me with a good concept behind Fourier transforms. Basically, I was handed a 10 page document with all sorts of mathematical wizardry going on, so that by next lecture they could use Fourier theory. I might have kinda understood the derivations, but I missed any visual intuition as to why Fourier transforms worked. After watching this video I went back to that document and it made a lot more sense. I believe many people just end up memorising the formula’s, without much understanding. It’s a lot harder to find new applications for a theory if you don’t really understand where it comes from and what makes it work.

@petermarsh4578 3 года назад

@@vapourmile I mostly agree with you here. The aim of the videos isn't to give a deep understanding, but to give the viewer a neat intuative sense of what's involved in the topic. However, I love these channels! It makes these difficult topics accessible for, well, anyone. And in my case, I often come to these sorts of channels to supplement my academic learning. I find lectures to be quite dry and difficult, but when I combine that rigorous understanding with this intuative understanding, that's when I'm most easily able to work with and exercise these ideas!

@henokhsihotang9291 3 года назад

@@petermarsh4578 Exactly, people often think that this is all formal academic course teaches you and say "school and college bad!!!". Videos like these are meant to explain the bigger picture of a subject, not to replace rigorous academic study of it. At best, these are meant so that the general public understands more (not all) of the topic, and as a "companion" for those studying it in an academic institution.

@Happyduderawr 3 года назад

i had some excellent professors, however it doesn't really matter too much if the professor is bad or not since learning math takes a ton of self study anyway. The people complaing about bad proffesors may have valid criticisms, but when you do research you're basically on your own and it doesn't really have much of an effect on your education, though all your colleagues will be massive math nerds.

@dombowombo3076 5 лет назад

I would love to see a video about the Laplace - Transformation. I´m very gratefull you are out there making videos about topics I´m often not able to fully understand myself. :)

@sdsa007 2 года назад

This is one of the best visualizations ever! and there was another Shakespearian one you made that is also marvellously insightful about vector spaces, awesome works of educational art!

@paopis Год назад

I want to cry for the beauty you manage to convey!

@stonail665 6 лет назад

Give this guy a Fields Medal for discovering the best way of teaching Mathematics.

@EDoyl 6 лет назад

Every time you upload a video I think: "eh, I've studied that before and these are supposed to work as an introduction for an unfamiliar audience, I'll listen to it in the background or something". And then every time it's a mind blowing approach. When you say something like 14:43 and I realise where you're going with it I'm always surprised and amazed at how elegant and cool you've made the topic.

@DeathBringer769 6 лет назад

That's why mental laziness and complacency is always a potential threat to any of us, even more so when you think "oh, I've already learned that" in your head, or you go "oh, I can't ever be mentally lazy; I have a college education and studied hard." I've been guilty of the same in the past sometimes but I keep these ideas in mind and actively try to be better. Remember: you ALWAYS have something more to learn. NEVER stop trying to learn more every day (or at least improve/further clarify your current understanding on subjects at the very least.) Having worked or studied hard in the past is no reason to get complacent in the *present* and think you're "done" already (that's just "self-justified" laziness, in my view.) That's the attitude I try to take at least ;)

@EDoyl 6 лет назад

Thanks for the input, Deathbrewer

@BritishBeachcomber 2 года назад

I've been designing electronics using the FFT for more than 40 years but this is one of the best explanations I've ever seen.

@mostafaabdein459 Год назад

Dude, Your work is so great that it seems almost impossible to me, you manage to simplify the most complex concept to a degree that was -for me- unimaginable, great job

@creepcreepier6082 3 года назад

I can watch it a hundred times and still not get tired of it. I can only imagine how difficult this would have been for me without this kind of explanation

@okktok Год назад

Because he is overly complicating the concept

@skylarkstarsmith3926 Год назад

I can watch it a hundred times and still not get it. :/ I just do not get this rotating spirograph thing at all.

@kin_1997 Год назад

Beautifully explained, second time watching the video and its starting to make sence, will be back again to further try and grasp the concept just as intuitively you make it seem to be. Your effect is forever appreciated 3B1B.

@Mnmunky 11 месяцев назад

This is an unbelievable video, explaining what I leaned a million years ago rote, into actual understandable terms. Thank you! When my son gets to this point in his math journey, I’m going to sit down with him and we will watch this together.

@opl500 6 лет назад

That has to be the best explanation of the Fourier Transform I've ever seen.

@Nachtgrabb 6 лет назад

I have a master degree in Mechatronics. I had lectures in Signal and picture processing. I learned how the transformation behaves, its properties and what happens if you change the function, shift, strech it etc. But nobody gave us an analogy to understand the tranformation formular itself. Thx man. Now I have a new perspective to this topic.

@lourias 2 года назад

If only this video had been published back in 2011... I kind of understood the sequence, but you adding the SOUND frequency portion now makes PERFECT SENSE!

@PiechureQ 2 года назад

Gościu, świetny film. Genialna reprezentacja całego procesu. Dzięki

@jayanths8526 6 лет назад

Life seems so simple and beautiful when I watch your videos. Thanks..

@ilovenomorepoetry 2 года назад

I'm just a musician wanting to understand more about sound...haven't done math since high school...this video was probably the first time I have enjoyed math...ever. Amazing stuff!

@donlevinson4645 Год назад

3b1b, really, you are some type of an angel. You fix the irreversible damage that highschool and academics cause you when they "teach" you math in most possible boring and non- intuitive way that there is. I cannot imagine the amount of effort you put into these types of videos and I really wonder where YOU studied math in such a way that makes it so clear and second-nature to you. Thank you a lot from the depths.

@vincentleone1833 Год назад

Outstanding Presentations! You were born to teach.

@NeilDeshpande313 6 лет назад

Your channel is LITERALLY more educative than all the universities in my country. Amazing. Your videos have seriously sparked my interest in mathematics.

@independentchannel844 5 лет назад

Neil Deshpande , yah bhai tune dil chune wala baat kaha

@rabbitpiet7182 5 лет назад

And what country is that then

@NeilDeshpande313 5 лет назад

Rabbit Piet India :)

@avatsavirs 5 лет назад

True that! I learnt more about Fourier transform in the first 10 minutes than I did in my entire second semester.

@daily8150 5 лет назад

The feeling when everything clicks in is amazing.

@Rebbyrag 6 лет назад

As an electrical engineering graduate I SERIOUSLY wish this had come out while I was still in college, SUPER insightful and it all comes together and makes SO much more sense now. I always thought of it as a shorthand "switch" back and forth between frequency and time domain, but the polar graph and Euler's equation makes SO much more sense.

@dp0813 6 лет назад

Josh Garber well, technically it IS a shorthand switch between freq & time domains, bc interpretation & manipulation are easier in one or the other domain, depending on the circumstances. But you're right; the explanation in this video is superb & goes beyond just freq & time domain.

@LinhTran-wr8bd Год назад

an eye opening! you make complicated things become much simpler and easier to understand. thank you!

@amyhughes2149 Год назад

This is going to be covered later in my uni course and this video makes me excited to get there. Math is so beautiful!

@softwarefac 6 лет назад

Every lecturer in my life has failed to learn me what Fourier transforms is but you did it in just 20minutes. Amazing!

@damianjurkiewicz3312 6 лет назад

I have Master degree of mechanical engineering and your videos helps me a lot truly understand math and physics. Thank you so much. Your brain is beautiful. Now I see that complex numbers nad FT it is just smart mathematical tool.

@anushka.narsima Год назад

omg from my math class i just remembered fourier transforms as 'some complicated looking integral formula that seems important' but I finally understand this wonderful topic now. Your videos make me value mathematical concepts so much!

@shwifty123 2 года назад

Came across the fourier transform in multiple seminars (pure math, diff eqs in physics & cs). Yet this video gave me a perspective I was missing for a while. Thanks!

@bane937 6 лет назад

This is priceless!!! This simply can’t be found in any book! Thank you for the time put in for sharing these beautiful ideas!! :)) Best regards!!

@wise_fool 6 лет назад

Branislav J precious*

@ImaginaryHuman072889 6 лет назад

actually, the fact the graph shows the spike at 0 when the sine wave is shifted up (because you don't want to deal with negative values) makes perfect sense, because this effectively is telling you that there is some 0-frequency (or "DC" in electronics) component to the signal. anyway, great video. as an EE who took all sorts of classes on this stuff in college, I still learned some stuff because these explanations and visualizations are amazing!