New video, Fourier transforms!
Added 2018-01-26 19:41:28 +0000 UTCHi Everyone,
It's been over a month since I posted, but I finally got around to one of the most commonly requested topics: Fourier transforms. Part of the reason for the delay is that the two new 3blue1brown team members just joined (thanks in large part to Patreon funds), so much of this month went towards on-boarding them. I'm really excited about the videos that each of them are working on, and I think you will be too once they're out.
As I say in the video, there is quite a bit more to say on the topic, so I'll do a second installation going into other places where this operation shows up. If there are any that you'd like to see in particular, now would be a good time to make the request :)
-Grant
Comments
What does it mean to find fourier transform for aperiodic signal(A pulse or a real exponential)??
Saketh Vns
2018-12-25 20:58:45 +0000 UTCThe single most amazing informational content about FT ever. of all time <3
Martin Embeh
2018-03-08 20:41:36 +0000 UTCSorry, little late to the party here. However, I'm so glad you're doing a series on the Fourier Transform! I became a much better student back in school after having a class unit all over this transform and it's derivation. I nerd-ed out pretty hard over this stuff, and still do! Great job, and I hope to see more transform methods (possibly?) in the future!
Britton
2018-02-18 21:58:48 +0000 UTCI have found part of this video has been uploaded to weibo.com by an Weibo account in China(this is the website that post the video <a href="https://weibo.com/tv/v/G0k10BRm7?fid=1034:a89ffd8c50c68244da66a7fac7d8345d)." rel="nofollow noopener" target="_blank">https://weibo.com/tv/v/G0k10BRm7?fid=1034:a89ffd8c50c68244da66a7fac7d8345d).</a> I assume that this kind of uploading could undermine the your intelligence property. Maybe we need to find a way to protect your property.
Weidong Chen
2018-02-09 04:48:01 +0000 UTChey Grant! I just want to know if you have any plans of making a video series on Conic Sections and what the equations actually mean, or consider making this series.
kiran ajij
2018-02-07 06:30:38 +0000 UTCThank you so much! Both for the pledge, and for the kind words :)
3blue1brown
2018-02-05 22:15:57 +0000 UTCYou’ve helped me more than you could ever know in my study of math before this video, but this one pushed me over the edge and got me to pledge. This video was such a brilliant masterpiece that it defies belief. By far your crowning achievement in my opinion.
Sachin Shukla
2018-02-04 22:41:34 +0000 UTCThanks so much! I really appreciate that, and I'll take note your request for Tensors.
3blue1brown
2018-02-02 20:00:46 +0000 UTCAlright I finally caved and supported after watching this video. You are by far the best channel on Youtube for intuitive understanding of maths concepts. Someone just mentioned in your comments but I heartily agree... A video (or series) on tensors would be an absolute godsend. Keep up the great work!
PeetieGonzalez
2018-02-02 13:18:06 +0000 UTCwell waddya know ... theatre mode is available if I watch same video on youtube channel. Strange, since even watching it on Patreon is also via Youtube.
Chris Jennings
2018-02-01 08:47:12 +0000 UTCHmm, I think theater mode is not something I have control over, but is on YouTube's end. If you're watching it on Patreon, I don't think it has a theater mode, but what happens when you watch it on YouTube?
3blue1brown
2018-02-01 02:07:06 +0000 UTCThanks for spreading the word! I think in the sequel series to Linear Algebra, I might talk a bit more about operators in infinite-dimensional vector spaces.
3blue1brown
2018-02-01 02:02:43 +0000 UTCNice! This is going to be a video I see myself sending people a lot... I'm also really hoping that one treatment of the Fourier transform is going to be about sine waves as a vector space.
Evan Miyazono
2018-01-30 18:15:47 +0000 UTCexcellent, really looking forward to the next instalment. One small comment: Your videos usually allow for "Theatre mode" but this one would only run full screen , or miniature. Hoping Theatre mode re-appears in subsequent releases ... PS: I would love to get your explanation of Fast Fourier Transforms (FFT) and Discrete Fourier Transforms (DFT) and when they should be used ... hopefully in a subsequent video :) On second thought maybe the sampled example in this video is a DFT?
Chris Jennings
2018-01-30 08:57:56 +0000 UTCAh, good feedback to hear. I did that recording with a slightly different mic setup, so I'll have to adjust things a bit more.
3blue1brown
2018-01-28 07:17:30 +0000 UTCThanks so much!
3blue1brown
2018-01-28 07:16:39 +0000 UTCWow, I was so happy to see a video about the Fourier Transform!!! This is the secret to understanding information itself which is why it is expressed in quantum physics as the uncertainty principle. Information is just patterns therefore randomness/noise is the opposite of information. The Fourier transform is able to translate these patterns between two domains of information. I'm raising my pledge because you did this video!
Benjamin BairMoshe
2018-01-28 06:39:04 +0000 UTCInteresting! I always thought the easiest way was to introduce the Fourier transform and then just ask what the normalized Fourier transform of a simple sin wave was, but I see your point.... Would love to see the introduction from the other side, in my experience physics undergrads always get confused when handling it
ChalkyChalkson
2018-01-28 04:12:26 +0000 UTCFirst draft of the script had mention of the dirac delta, but it seemed too beside the point for the main goal here. I think I would only feel comfortable talking about it in the context of a measure. One day!
3blue1brown
2018-01-28 03:36:25 +0000 UTCOne of Mathologer’s best!
3blue1brown
2018-01-28 03:34:20 +0000 UTCHaha, not intentionally, but the default is for the middle one to be the one asking a thing.
3blue1brown
2018-01-28 03:33:19 +0000 UTCHi, as ever a great job, and very enjoyable. However, I found the sound quality took away from my enjoyment as it seemed quite muffled. In the section at the end you can hear the audio quality change becoming more crisp. It seems a shame if your audio is not at the same high standard as the video. Thanks for the good work!
Scott
2018-01-28 00:07:47 +0000 UTCWill you actually prove the inverse formally, Grant? Or just show the intuition? I personally think a formal prove might be counter productive here as the ones I am aware of aren't very nice :/
ChalkyChalkson
2018-01-28 00:03:06 +0000 UTCI don't know if you know a some calculus and algebra, but there is a super easy (but non visual) way to look at Fourier transforms in terms of scalar products in the infinitely dimensional C vector space of functions with finite integrals (as I said, not visual :P )
ChalkyChalkson
2018-01-28 00:00:35 +0000 UTCI promise it here and now: I will increase my pledge if you manage to explain the dirac delta to a general audience in a way that doesn't leave everyone confused! (See it as a bet/dare) Speaking of which: 17:00 is a way better explanation of why F of the dirac delta is a planar wave than I have ever heard before, just sad you didn't include it as a note. At this point I can really see you do a "maths of QM" series. I mean commutators, Fourier transforms, hilbertspaces, all really cool concepts! Oh, and this episode was definitely worth my omega/f $
ChalkyChalkson
2018-01-27 23:56:23 +0000 UTCI would love to see discrete transforms specifically how they are used in image processing.
Jeff Barbose
2018-01-27 19:20:49 +0000 UTCThat's awesome to hear that you've begun your expansion!
Magnasium
2018-01-27 16:46:22 +0000 UTCThanks for the awesome work as always. Just want to add that I found this video especially enlightening viewed in conjunction with Mathologer’s video on “Times Tables, Mandelbrot, and the Heart of Mathematics”. <a href="https://m.youtube.com/watch?v=qhbuKbxJsk8" rel="nofollow noopener" target="_blank">https://m.youtube.com/watch?v=qhbuKbxJsk8</a>
Steven Soloway
2018-01-27 16:13:59 +0000 UTCI would also point out that there are fewer good visual representations of the Laplace Transforms out there. Or in other words, if I may, there is a need for your touch applied to the LT
Dan Steinitz
2018-01-27 12:48:10 +0000 UTCIf you aren't familiar with it, one of my favorite "pop-maths" books is "Journey Through Genius". It basically takes the 10 or so "best" proofs in mathematics, and gives their history, their importance, etc. But crucially, the author actually goes through all the maths necessary to understand the proofs! This turned it from a regular "pop-math" book which I also love, to something far better - something between a history and a textbook. I think the reason this is so important is because we have textbooks, and we have pop-science/pop-math books that explain things without the details, but there are far fewer resources that do the in-between thing that you're doing. That's what *I* love about it, anyway - I feel I get a better understanding vs the normal "handwavy" explanation, but I also get the intuition and importance of the material that so few textbooks manage to get right.
Edan Maor
2018-01-27 12:47:37 +0000 UTCAlright. Not being an engineer but a math PhD, this request may be less interesting but here it is: if a function is highly “wild” then its Fourier series decays slowly as f -> infinity, but if it is smooth then the series decays rapidly. In fact, the smoother, the more rapid. As an application of this, you can demonstrate a nifty way to construct wild no-where differentiable functions - simply take a random Fourier series that decays sufficiently slowly.
Jacob Mirra
2018-01-27 11:53:20 +0000 UTCA series on ODEs would be fantastic since I haven’t learn the relation berween matrices and ODES
Owen Allemang
2018-01-27 11:07:42 +0000 UTCThanks for another great video Grant. It would be great if you could touch on Fourier series too and the idea of basis functions.
Ehsan Montazeri
2018-01-27 09:34:19 +0000 UTCGreat stuff and thanks for making a video on it. I came across the idea (tinyurl.com/y9q9yucx) when I was learning about Fourier Transformations at the university and the concept immediately clicked in my mind. I think your video format is the perfect setting for explaining the concept in video form. I will show it to my students! A completely unrelated question which popped into my mind when the middle "Blue" asked a question at 7:57: Have you assigned some consistent personality to the three blues (intentionally or otherwise)? E.g. is the middle one more likely to ask questions, the right one more likely to need a second explanation and so on?
Vidar Skogvoll
2018-01-27 09:28:34 +0000 UTCwow! Tks! That was awesome!
Daniel Armesto
2018-01-27 08:55:35 +0000 UTCLaplace transforms are also one of the most commonly requested.
3blue1brown
2018-01-27 08:43:21 +0000 UTCI think that could be very satisfying, yes.
3blue1brown
2018-01-27 08:42:59 +0000 UTCIf only I had also covered inverses in full today!
3blue1brown
2018-01-27 08:42:28 +0000 UTCIn thinking about getting math out to more people, it's certainly tempting to shirk away from equations, for fear that too much notational density will send people away. But it seems people really find it empowering when they know how to make a given equation come to life, which has been one of the goals of the channel.
3blue1brown
2018-01-27 08:40:55 +0000 UTCThanks :)
3blue1brown
2018-01-27 08:38:05 +0000 UTCOh cool, I'll look more into that!
3blue1brown
2018-01-27 08:37:55 +0000 UTCThe best intuition I know of for trace is in the context of phase flow for linear ODEs, where there is a relation between the trace of a matrix defining a given set of linear differential equations, and the determinant (as a function of time) of the solution to the equations. So, that being said, perhaps in a series on ODEs one day!
3blue1brown
2018-01-27 08:37:29 +0000 UTCYou requested suggestions, so what about doing videos on the other transforms, such as Laplace and wavelet? I can only imagine how amazing the explanation and intuition you will be able to extract using the framework you developed to explain Fourier transform.
Eduardo Diniz
2018-01-27 00:53:21 +0000 UTCI was talking with a friend today and said to him: "hey, you know, I can calculate Fourier transform and I can calculate the inverse with no problem, yet I watched every video on youtube explaining it and still have no idea what is exactly happening!". Then now I come home and this comes in my notifications, I was never so excited for a video as this. You are amazing man, Thank you.
Mohanad Marwan
2018-01-26 23:48:52 +0000 UTCI was hoping that was the reason. Excellent video - one of the best. Love that you went the extra step to derive the formula. Can you do that for the normal distribution when you continue your probability series?
Daniel Raynaud
2018-01-26 23:10:41 +0000 UTCWhen editing 2D images, It's possible to use the fourier transform to do: - Remove High-frequency detail (eg. pores on the face) without blurring the color of the pore into the surrounding pixels. - Transfer a high frequency texture (eg. a rough wall surface) from one material onto another. In 3D computer graphics, there are Spherical Harmonics which can be used to describe light from all angles without special behavior at the poles of the sphere. silviojemma.com/public/papers/lighting/spherical-harmonic-lighting.pdf
DomNomNom
2018-01-26 22:11:05 +0000 UTCGreat to hear that you've gotten team members! Looking forward to seeing more content.
Kevin Strehl
2018-01-26 21:32:27 +0000 UTCAbsolutely brilliant. I've read dozens of explanations of Fourier transforms, but none of them come close to this. I really love how you both gave the intuition behind it, but also tied that intuition into the math itself. Your specialty of course :)
Edan Maor
2018-01-26 21:14:41 +0000 UTCExcellent explanation; classic 3b1b! Looking forward to the continuation of this.
Dan Davison
2018-01-26 21:07:52 +0000 UTCHey Grant! I think a really interesting idea to discuss when explaining Fourier transform is the idea of noise. Using Fourier transform, you can distinguish between different types of noise (white, pink, ...) and a really cool result that noise in nature always follows a simple 1/f curve in the frequency space. Great video btw!
Aakash Lakshmanan
2018-01-26 20:23:29 +0000 UTCHi Grant, I would like to have a way to visualise the trace of a given matrix and also visualise symmetrical matrices, I think you could do an amazing job explaining it, as always. I have been studying those (trace, symmetrical matrices and isometry) in prépa (before engineering school in France) for two weeks now, and I still don't have an intuition for it.
Owen Allemang
2018-01-26 19:56:34 +0000 UTC
