> analyse > analyse-fonctionnelle > transformations > analyse-harmonique > visual-introduction-to-fourier-transform-3blue1brown

But what is the Fourier Transform? A visual introduction.

3Blue1Brown - 2018-01-26

An animated introduction to the Fourier Transform.
Home page: https://www.3blue1brown.com/
Brought to you by you: http://3b1b.co/fourier-thanks

Follow-on video about the uncertainty principle: https://youtu.be/MBnnXbOM5S4

Interactive made by a viewer inspired by this video:
https://prajwalsouza.github.io/Experiments/Fourier-Transform-Visualization.html

Also, take a look at this Jupyter notebook implementing this idea in a way you can play with:
https://github.com/thatSaneKid/fourier/blob/master/Fourier%20Transform%20-%20A%20Visual%20Introduction.ipynb

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Animations largely made using manim, a scrappy open-source python library.  https://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:
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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 YouTube, 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: http://3b1b.co/recommended

Various social media stuffs:
Website: https://www.3blue1brown.com
Twitter: https://twitter.com/3Blue1Brown
Patreon: https://patreon.com/3blue1brown
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Reddit: https://www.reddit.com/r/3Blue1Brown

Zubzub343 - 2018-01-26

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.

Marek Czarnecki - 2020-02-08

Totally agree. Gonna go through the videos to see if there is one explaining Euler's Identity !

Shukla Maths Academy - 2020-02-21

Nice

Sammy L - 2020-02-22

Because he’s not a teacher. He teaches well.

DSM 5D - 2020-03-03

If there is no profit motive involved, would you want to learn Manifest Math? So simple to grasp, and STILL perfectly applicable to applied science, but the notation built since it has been lost is, by self definition, irrational. Have you noticed how quickly new astronomical phenomena are being reinterpreted? Ever wonder how you happen to be alive at the right time to see the limits of "official" math and science? Would you buy a consciousness membrane mirror? Oh wait, you already have one. What math is driving and building these devices and their real-world, 3D implications? 2D binary digital gradient descent IS how math and physics is done, and it is a Math to the 2-3D confusion. I'm curious how a real person working in this architecture sees this criticism. We all start with what we are given, and choose from a set of options. Success is in part socially defined.

Varun Arora - 2020-03-08

3Blue1Brown ... when we think of the fourier transform integral, it is a complex integral and would give a complex number as a result. How does the real part of that result give me fourier transform as shown by x component in video

Daniel C - 2019-03-04

I declare you God in the realm of YouTube Education.

Michael Cornell - 2019-09-04

You sir, should educate the educators on how to pack and idea, then unpack it, my lord that was an enjoyable experience!

SAI VAMSI ANDIBOYINA - 2019-09-14

@David Nguyen 3blue1brown used to explain in khan academy too

Tobias Yoder - 2019-11-24

@David Nguyen ha... ha... ha...now thats a funny one xD

Long Nguyen-Vu - 2020-03-06

@David Nguyen nah Khan's explanation is never this clear and satisfying. Khan has a vast knowledge, I agree, though.

TheCDAGR81 - 2020-03-06

@David Nguyen Khan academy definitely doesn't go into much detail.

Manjunath Marakal - 2019-03-14

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

Evan490BC - 2020-01-04

This representation is what we call a "phasor" in Engineering, if you recall.

b888 - 2020-01-04

@Evan490BC OFC!

b888 - 2020-01-04

@Evan490BC phasor diagrams, it's all coming back!

Ashutosh Srivastava - 2020-03-04

@b888 he's trying to say that he has completed his engineering 13yrs ago.order of words may give an impression of what you said

Fernando Bustamante - 2020-03-07

the same statement I've done to my fiance immediately afterwards I've finished watching this outstanding video!

Vaibhav Tiwari - 2019-06-03

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

GubeTube19 - 2019-12-18

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

Sunny shah - 2019-04-29

If you can't explain it simply, you don't understand it well enough.
Albert Einstein was so right.
Our professors don't understand these stuff well enough, that's why they can't even explain it simply even though they have a whole semester, and hours and hours of daily lectures to teach.
While 3B1B explained it in about 20 minutes

William Taylor - 2019-12-07

@James Schneider "there are more important things to do" than teach the one they suppose to teach? That just shit!

Peshal Dahal - 2019-12-11

@Salvador3158 i was gonna write this :D

Anders - 2020-01-27

YOUR professors maybe.

Facce Bookk - 2020-03-06

Mostly, the problem is not in understanding, but in a talent to teach. I had a professor, in that time middle 90ties who was second most quoted Europa scientist in fluid mechanic field. But if you listen his classes it look awful, like man doesn't know what he is talking about. It doesn't mean that excellent scientist must be a good teacher, so that "If you can’t explain ....." do not hold the water. Here is a century challenge. Let somebody explain, in a common words, on a average academic level, Poencares Theorem, and after that Pelerman's 1200 sheets proof.

Bigyan Chapagain - 2020-03-08

and the more funny part is they want us to prove ourselves in a 3 hours exam!

LordFennel - 2018-01-26

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.

Anonymous squirrel - 2018-10-31

This video won't help you solve that exam.

Teresa Slaven-Blair - 2018-11-19

"They are spoken about in hushed tones like a mass genocide in the recent past." That made me laugh out loud at my desk cubicle! It's so true! hahaha

rightyourwrong - 2019-10-07

neverforget...

fuzzywzhe - 2020-01-20

Fourier transforms allows analysis of a circuit by just working with sin and cosine, provided it's a linear circuit.

Anders - 2020-01-27

No you're not better informed than when reading an actual textbook. His videos are cool and good for intuition, but that's it. He can't teach you to do a fourier transform, you need to open the textbook and do the exercises yourself.

Guy VanBuren - 2019-06-09

You now have an electrical engineering degree

BigFarma - 2019-10-09

Perfect

Vishnu Kumar - 2019-03-04

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

Hooterr - 2019-10-07

People with perfect pitch have just Fourier transformer built-in in their brain

Ngô Tùng Dương - 2019-10-17

I guess not many people get it. Luckily you have me!

Sofia - 2019-11-21

I like how you think

letslike15 - 2019-11-28

*Inverse Fourier Transformer
Since they would be thinking of that one note/frequency, they want to sing and execute it perfectly.

obiwac - 2019-12-26

We all have tho

chronic reverse - 2020-01-12

I immediately thought of this lol

CAPITALUST - 2019-04-07

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

Aditya Santhosh - 2019-04-18

@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

LOL Science - 2019-03-06

How can I double subscribe?

MrExtremehustler - 2019-05-14

@Saurabh Easy. Unsubscribe, than resubcbribe.

Emil S. - 2019-08-28

@Aditya Santhosh Beat me to it.

shrdlu - 2019-10-11

Binge watch all the videos

Zeus Thor - 2020-02-27

Make another gmail account to subscribe again

Bigyan Chapagain - 2020-03-08

hit the bell icon! LOL

Dombo Wombo - 2019-03-06

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. :)

Reaping Shadow - 2019-12-18

actually, why this winding around a circle part had never been mentioned in school???

Bigyan Chapagain - 2020-03-08

only if our teachers knew it! LOL

Siva rajan - 2019-05-30

4 years of college could take a nice slap on the face for not delivering the content to me in this way!!!! Dude you just made my worst fear to my favorite subject!!!!

pranit pawar - 2018-06-03

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

davidtheguitarman - 2019-01-09

For real.

Arjun Sohal - 2019-01-16

@John Michael It is obviously implied that he is talking about mathematics.

Adam Nasir - 2019-02-21

Mr. Michael,

I am aware that the relevance of this conversation has faded into obscurity for some months now, but as the man who lit a match and returns now to a house in flames, I feel obligated to share a few final opinions.

My issue is not with your demand for excellence from your students, as this is an area in which I would tend to agree with you. Despite the fact that I am of a younger generation, I am not, as you have put it, a “snowflake.” At the risk of sounding pompous, I am a very capable student who believes a grade is not an entitlement, but something to be earned.

Nor is my issue with your offering corrections to Pranit. I, too, observed the error in his comment and chuckled a bit internally. Had your comment not already been present, I might have even said something myself.

My issue, rather, is with your clear displacement of anger. Your initial response to Pranit established an extraordinarily irate tone, and from what I have read over the past few minutes, you maintained the same tone throughout this whole conversation. I am of the opinion that such a manner of speech is completely needless in this scenario, and it likely stems from the fact that you are disappointed about the education system. Based on what I’ve noticed about my peers’ behavior, you certainly have a right to be—students groveling for grades they didn’t earn and thinking they should be given the benefit of the doubt at all times is doubtlessly annoying. This, however, does not seem to justify calling complete strangers “not college material” or “dimwits” based on hardly any interaction at all.

I’m fully aware that you may respond to this with another irritated message frought with CAPITALS or “quotation marks” in order to call me sensitive, or entitled, or a moron, or any other phrase of your choosing. I am also fully aware that you may not reply to this at all. Whatever the case, I urge you to practice tolerance towards those who are not at fault for your personal and professional woes.

Thank you for your time.

ItsAllUnity - 2019-04-22

John Michael got all the attention. I think that is what he wanted. :DD

qwerty - 2020-01-27

@John Michael Your Dad sir should hv pulled out a last second.
He could hv done this world a huge favour.
Now go.Find grammar mistakes for your ego.
Again your dad sd hv pulled out.

Sandra Braithwaite - 2019-12-14

we are truly fortunate to live in a time where we have creators that can use computer graphics to display physics concepts so elegantly. well done

P K - 2020-01-04

Sandra took my Braith Awaiyyyyyyy........te

Accelerator - 2020-02-19

@P K k

Sunny Rajkarnikar - 2019-12-26

i know what you did there at 11:52 "its a little more COMPLEX than this x coordinate of center of mass idea "

bolin Li - 2020-03-06

I really like math, even I just learen at high school. it is so magical ,beautiful, your video is perfect

Aryam Sthapak - 2019-10-02

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

Abdul-Kareem - 2019-10-14

I watched this video for the first time about almost 5 months ago, and literally didn't get anything about the idea, maybe because I had confronted the computation involved in Fourier Transform in one of my courses last year. But I knew this video explains something beautiful. Luckily, I kept watching it again and again, sometimes closing the tab because almost nothing made sense to me. But every time I watched it, I got a step closer. I could feel that. And today when I opened the tab, I thought 'how can I not understand this step-by-step conceptual story', and then I paid full attention from the start, pausing when I needed to make things clear in my mind. And yes, I am here now. Grabbed this great idea thankfully! This gives me a feel of satisfaction.

John Spencer - 2020-02-15

hard work is food for the soul

ZZ ZZ - 2019-04-01

I want to go back to college and do all my EE courses again, I would be getting all A's today

Carl Grainger - 2019-05-02

Maths with pictures - that’s my kind of learning. Thanks so much

Lotus Pirate - 2019-05-21

This video is possibly one of the best math videos that I’ve seen in forever. Bravo sir, incredibly concise and intuitive explanation.

gonzaloberasaluce - 2018-01-28

Your videos sir, are a gift to humanity

berbudy - 2018-02-04

so true, I'm so glad this guy exist

Jorge C. M. - 2018-02-05

berbudy exists*

Sameer Ansari - 2018-03-26

So Trueee...!!!

BMM Productions - 2019-12-05

I've had good teachers but this guy is on another level

Lucas Barroca - 2019-12-01

Please talk about Laplace transform too, I really would like to know where this transform come from

Ananyapam De - 2019-06-29

When he first said complex numbers, i was so excited and was hugging my pillow. Thank you sir

dario dal cin - 2019-09-13

"this is a pure A"
Talks over it

agvil fernandes - 2019-03-02

Oh my God!!! I didn't understand Fourier transforms throughout engineering, this video explained it like its basic addition...

M4m4 Lu191 - 2020-02-15

speaker: high pitched demonic screeching
pi: 😡

TheAzylum - 2019-12-07

wow, i never really considered how simple it really is, and it just makes so much logical sense as to where the formula comes from. Thank you so much for teaching me this.

Neto r g - 2019-12-10

The way you manage to interpret and unwind such concepts it's just genius, love your channel and the effort putted in it is just so clear and outstanding. The illustrations you make are just invaluable! Thank you

afwaller - 2019-09-01

This is literally the best explanation I have ever had of something I thought I already knew but did not understand as well as I did until I watched your video.

Anna Nkldun - 2019-12-26

Do you have a link to the explanation that is figuratively the best?

Andrea Haider - 2019-06-08

"it's in the direction of truth" :D

Aleksander Kulewski - 2020-01-19

I love that "BUT!" at 5:25 <3

Kunal Nayyar - 2019-12-15

I've always heard about the fourier transform and tried to wrap my head around it but nothing made me understand as good as this video did . I am surely jealous of that beautiful mind of yours grant :(

macronencer - 2018-02-01

I think you might be the best communicator on YouTube. 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!

Michal - 2019-01-19

@Nothing\ These guys are just grasping at the illusion of understanding. They felt like they learned something and thought it was flawless lecture but are probably the same kids who didn't pay attention in class. Learning isn't about entertainment, it's about understanding and just because you feel like you learned a lot doesn't mean you did.

Naif Alkhunaizi - 2019-02-01

Michal Kalita can't agree more! It's easy to fool yourself ;)

ps200306 - 2019-02-24

There is no one presentation that can capture all the concepts, let alone one that can do it at the right level for every viewer. I think some people are expecting too much. If you wanted stuff about unit circles and rotations in the complex plane, there was a link embedded in the video to a separate presentation on that. If you wanted a fully academic presentation consult a textbook. All I can say is I've already studied Fourier transforms academically, and understand that they translate from the time domain to the frequency domain, but I never had that intuitive understanding in terms of the "winding machine" concept. Even though I already knew more of the math than this video goes into, I think I now understand it a lot better. Thank you.

Synaxis - 2019-02-27

flawlessly

Jan Hus - 2019-03-03

Tears of joy... If only this guy was my math teacher in grad school

Not Agrim - 2019-12-12

14:00 I never knew i was so addicted to counter clockwise...

glasslinger - 2019-12-14

Gee, I'm so lucky that my most in depth thought is when I will eat next!

Damjan Tasevski - 2019-09-30

This is pure gold, thank you so much I finally understand it now

Surya E R - 2019-07-03

XD I learnt yesterday about Amplitude modulation -scattering equation using Fourier
coincidence ?

MisterMcHaos - 2018-01-27

Sometimes - just sometimes - one needs access to a "double like" button.

Well done, 3B1B.

HattoriHanzo62 - 2018-01-30

Yep, one per turn :-)

öafhaüohgüoihgäkds - 2018-01-31

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

TPK's Channel - 2018-02-06

The other like button is in the complex plane, hence we are not able to access it. :P

Diego Mondéjar - 2018-02-07

MisterMcHaos Patreon...

Kit Laughlin - 2018-02-10

Or just hold it down. This is the best exposition on FTs I have ever seen; deep thanks.

Tor Bruheim - 2019-06-01

I was trying to solve this by my self, and thought thought this problem in a much more complex way. This solution is brilliantly solved.

Nima - 2019-04-01

Bless you! I am clinician trying to understand deep learning methods as applied to clinical data and needed to brush up on these topics!

Saeed Masoumi - 2020-03-08

oh boy, math is freaking sweet and you put icing on it.

Thanks for the great video.

AuroraClair - 2019-08-16

It's so frustrating when I stumble upon an interesting video I'd really like to watch, but have to mark it as 'watch later' because I'm running late on other stuff x//
Edit: but I definitely WILL watch this later!

Jetset Willy - 2018-01-27

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

Mau365PP - 2019-03-10

As a mechatronics engineer student all I can say with my dropped jaw is: thank you !

Eve - 2020-03-06

What does 'intensity' mean, in terms of the label for the y-axis of the original waveform graph?

김바쓰 - 2020-03-07

Maybe.... I can make the program about Equalizing in sound player by using little fourier series.


1. Divide original sound pulse into sine waves.
2. Select frequency.
3. Calculate(* or /) coefficient at selected sine wave.
4. Sum all sine waves.