The Remarkable Story Behind The Most Important Algorithm Of All Time

The Fast Fourier Transform is used everywhere but it has a fascinating origin story that could have ended the nuclear arms race. This video is sponsored by 80,000 Hours. Head to 80000hours.org/veritasium to sign up for their newsletter and get sent a free copy of their in-depth career guide.
A huge thank you to Dr. Richard Garwin for taking the time to speak with us.
Thanks to Dr. Steve Brunton of the University of Washington for his help with understanding the Fast Fourier Transform.
Thanks to Dr. Cliff Thurber of the University of Wisconsin-Madison, Dr. Paul Richards of Columbia University, and Dr. Steven Gibbons of the Norwegian Geotechnical Institute for their expertise.
Thanks to Grant Sanderson of 3Blue1Brown for his helpful feedback on the script. His great video on the Fourier Transform is here - • But what is the Fourie...
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References:
Kristensen, H.M., Korda, M. (2022). Status of World Nuclear Forces. Federation of American Scientists (FAS). ve42.co/Stockpile2022
Barth, K. H. (1998). Science and politics in early nuclear test ban negotiations. Physics Today, 51(3), 34-39. - ve42.co/Barth1998
Schmalberger, T. (1991). In pursuit of a nuclear test ban treaty - ve42.co/Schmalberger1991
Bowers, D., & Selby, N. D. (2009). Forensic seismology and the comprehensive nuclear-test-ban treaty. Annual Review of Earth and Planetary Sciences, 37, 209-236 - ve42.co/Bowers2009
Incorporated Research Institutions for Seismology (IRIS). (2022). How Often Do Earthquakes Occur? ve42.co/IRIS2022
Kimball, D. (2022). The Nuclear Testing Tally. Arms Control Association. ve42.co/TestTally2022
Kværna, T., & Ringdal, F. (2013). Detection capability of the seismic network of the International Monitoring System for the Comprehensive Nuclear Test Ban Treaty. Bulletin of the Seismological Society of America, 103(2A), 759-772 - ve42.co/Kvrna2013
Sykes, L. R., & Evernden, J. F. (1982). The verification of a comprehensive nuclear test ban. Scientific American, 247(4), 47-55 - ve42.co/Sykes1982
Peterson, J., & Hutt, C. R. (2014). World-wide standardized seismograph network: a data users guide (p. 82). US Department of the Interior, US Geological Survey. - ve42.co/Peterson2014
Richards, P. G., & Kim, W. Y. (2009). Monitoring for nuclear explosions. Scientific American, 300(3), 70-77 - ve42.co/Richards2009
Jacobsen, L. L., Fedorova, I., & Lajus, J. (2021). The seismograph as a diplomatic object: The Soviet-American exchange of instruments, 1958-1964. Centaurus, 63(2), 277-295 - ve42.co/Jacobsen2021
Schwartz S. I. (1998). The Hidden Costs Of Our Nuclear Arsenal: Overview Of Project Findings. The Brookings Institution - ve42.co/Schwartz1998
Ricón, J.L. (2016). The Soviet Union: Military Spending. Nintil - ve42.co/Nintil2016
Heideman, M. T., Johnson, D. H., & Burrus, C. S. (1985). Gauss and the history of the fast Fourier transform. Archive for history of exact sciences, 265-277 - ve42.co/Heideman1985
Ford, D. (2004). Richard Garwin - Session IV. American Institute of Physics (AIP). - ve42.co/Ford2004
Aaserud, F. (1986). Richard Garwin - Session I. American Institute of Physics (AIP). - ve42.co/Aaserud1986
Goldstein, A. (1997). James W. Cooley, an oral history. IEEE History Center, Piscataway, NJ, USA - ve42.co/Goldstein1997
Cooley, J., Garwin, R., Rader, C., Bogert, B., & Stockham, T. (1969). The 1968 Arden House workshop on fast Fourier transform processing. IEEE Transactions on Audio and Electroacoustics, 17(2), 66-76 - ve42.co/Cooley1969
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Special thanks to Patreon supporters:
Louis Lebbos, Elliot MIller, RayJ Johnson, Brian Busbee, Jerome Barakos M.D., Amadeo Bee, TTST, Balkrishna Heroor, Chris LaClair, John H. Austin, Jr., OnlineBookClub.org, Matthew Gonzalez, Eric Sexton, John Kiehl, Diffbot, Gnare, Dave Kircher, Burt Humburg, Blake Byers, Dumky, Evgeny Skvortsov, Meekay, Bill Linder, Paul Peijzel, Josh Hibschman, Mac Malkawi, Mike Schneider, John Bauer, jim buckmaster, Juan Benet, Sunil Nagaraj, Richard Sundvall, Lee Redden, Stephen Wilcox, Marinus Kuivenhoven, Michael Krugman, Cy 'kkm' K'Nelson, Sam Lutfi, Ron Neal
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Written by Derek Muller & Felicity Nelson
Filmed by Derek Muller & Raquel Nuno
Animation by Ivy Tello, Jakub Misiek, Alex Drakoulis, and Fabio Albertelli
Edited by Albert Leung & Derek Muller
Research Assistant: Katie Barnshaw
Additional video/photos supplied by Pond5 and Getty Images
Music from Epidemic Sound
Produced by Derek Muller, Petr Lebedev, and Emily Zhang

[@veritasium]

If you're thinking about how to make a positive impact with your work, get a free in-depth career guide from 80,000 Hours: 80000hours.org/veritasium

[@ThatDude_OverThere]

Thanks.

[@d.bcooper2271]

Atheists claim that they are intellectually superior to religious people because they are willing to question their beliefs, whereas religious people are dogmatic and refuse to question their deepest beleifs and won't consider evidence that could potentially undermine those beliefs. Well, have you ever heard an atheist say: "I wonder if constantly increasing individual freedom is a good thing." "I was wrong about democracy being a viable system." "Maybe the sexual revolution was a mistake." "The evidence shows that equality of the sexes is destructive." "Let's have a debate on if freedom of speech and religion are good for society." "Could it be that women need fewer rights?" I have literally never seen an atheist raise these questions or hold these positions up to serious scrutiny. Nor do they provide any evidence for their beliefs on these matters. They simply assert them and ridicule and mock anyone who disagrees with them.

[@apoorvshah2144]

Why you changed the title and thumbnail, it was pretty cool

[@unaidhoore4031]

thank you

[@ghdrnrla11]

Oh!!!!!!! This is the most understandable Fourier video I've ever seen.

[@Davide_LP]

I can't believe how intelligent Gauss was, it's just incredible

[@jimboslice4468]

hence the phrase "he's good but he's no Gauss"

[@markarca6360]

It is related with his works on magnetism.

[@1aboPLZ]

@Don't read profile photo ok

[@dsdsspp7130]

here's another example of Gauss being a pure genius: "The Prime Number Theorem was conjectured by Legendre in 1798 and proved a century later by de la Vallee Poussin and Hadamard in 1896. However, after his death, a notebook of Gauss was found to contain the same conjecture, which he apparently made in 1791 at age 15. (You sort of have to feel sorry for all the otherwise “great” mathematicians who had the misfortune of being contemporaries of Gauss.)"

[@muttonface9032]

I’m smarter

[@developersteve1658]

I really can't overstate how appreciative I am of these science history videos. It's easy in the STEM fields to forget the history soaked into the ideas we take for granted every day. I would like if Math classes gave a little glimpse into this - especially in primary schools. Maybe more kids would appreciate the importance of math and "when we would ever need this in real life".

[@jeffbenton6183]

Same. I'm a huge history nerd, and it wasn't until college, when I took history of math courses that I really began to appreciate how awesome Math is and became somewhat close to actually being good at it (though I always knew it was important). If math had been taught to me that way at a much younger age, then I might've developed more math-friendly habits early enough that I could actually be a "math person" today.

[@patrickjordan2233]

The current generation of teachers (@ any given point...) are the product of their own teaching/grasp of context. Oddly, it wasn't my history teacher, but my English teacher in HS in the 80's who was intuitively combining Core principles (cross-disipline teaching).. Fun class, cool trivia that Really pulled one in... Thanks, Mr Murphy. 🙏

[@davidadams2395]

@@patrickjordan2233 You were fortunate, then. My teachers in the '80s made the subject as dry as the chalk in their hands. Math taught with the same enthusiasm as Ben Stein in *Ferris Bueller's Day Off* shut me off completely.

[@426F6F]

Yess, Math history actually sounds interesting too

[@Sinzari]

I think if taught in schools, kids would just fall asleep. The important part, as Veritasium has discovered, is being able to be a good storyteller. There's a reason Derek has a PhD in Physics Education, he's basically spent his life on being able to teach STEM this well. I wish it was possible to have a Derek in every class, but unfortunately it's not. A good alternative though, might be for school boards to commission videos like this that teach the curriculum in more interesting ways. And there's already evidence this works, via Bill Nye the Science Guy. Who can say they actually disliked him or got bored of his videos as a kid? Not many, if any. If all of STEM was taught so interestingly, with stories that pique curiosity and experiments that amaze kids, less people would find STEM boring or difficult and more would find it a place to explore. IMO at least.

[@XwitterEye]

imagine discovering the FFT and not bothering to publish it. legend

[@StrikeWarlock]

Gauss couldn't imagine it either. He was a perfectionist. The formula for FFT was one of the many incomplete papers he didn't publish, there were many more.

[@AA-ke5cu]

👽we do it all the time. Some things humans should never understand. Like how we shut down their nuclear launch facilities.

[@RandomAmbles]

Fuckin' Gauss.

[@Cvjkncfxcccfdd]

Absolute sigma

[@matthewbriggs9414]

Classic engineer

[@kartefact]

I wish I had this when i was in college studying DSP. Had no idea back then where and why this was used and we were only cramming the theory for the exams. This is probably one of the best visualisations of FFTs that I've come across. So simple to understand such a complex topic. This will help students of the subject understand the theory so much better when its real world application is known and its impact.

[@abiofficial-ws7pn]

We remember during our engineering, our maths professor just came in, just wrote and wrote nonstop on the board. The writing was so fast that we named him "machine gun" (the sound of the chalk on the board made rat-a-tat-a-tat-tat sound like that of a Thompson Machine gun). At that time we wondered why we were being taught this esoteric technique.

[@prasunbagdi6112]

That's Indian education for you

[@LaBamba690]

That's the difference between good professors and mediocre ones. Thank goodness I had an excellent professor for communications theory.

[@amardeep46]

Ah the dreaded DSP !

[@athena_03]

Thank God ! DSP and this video came at same time for us.

[@kronos2979]

Gauss discovering FFT even before Fourier published transforms is the most chad moment in history

[@reiter155]

Dude literally doodled on his notebook and said trash

[@googiegress7459]

@@reiter155 Wiped his swan's beak with it, wadded it up, and used it to light a giant blunt.

[@mide8845]

But he was kinda built different

[@amazingdude9042]

Soviets were fully right. USA never fulfilled any treaty at all in entire history. If soviets never had NUKES then they would be obliterated from planet earth and cut into 50+ smaller weak nations which would be USA puppets only.

[@MrPoornakumar]

kronos Jean-Baptiste Joseph Fourier, author of the analysis in his name, had the greatest impact on Science (& Technology now) like none else among the Scientists. There seems to be no alternative to Fourier's track.

[@MassimilianoCerioni]

I am a sound engineer, I work a lot with DSP. Knowing the background story of the FFT, and having it explained so smoothly leaves me speechless, you did another masterpiece. Thank you!

[@boraned]

haven't heard such profession, can you explain a bit, tell things about it and job opportunities?

[@friendlyone2706]

@@EdWeibe No, he is probably an ordinary student, possibly college level and definitely brighter than average that he both watched this and read the comments. . Be thankful for your professors and the environment in which you live.

[@friendlyone2706]

@@EdWeibe When you finish laughing, give Boran a couple well chosen sites you believe best exemplify your profession.

[@barthchris1]

@@EdWeibe Why did you even make such a immature comment, what is your motivation? What are you, 10?

[@SuperMonibuvy]

​@@EdWeibe This has got to be one of the most pedantic and immature comments I have ever read. Have you ever interacted with the general public at all? I wouldn't be surprised if less than 10% of the entire world population knew of DSP. Get off your high horse and go sit in the corner and think about what you've done.

[@sarthaksingh2852]

I am an electronics and communication student studying digital signal processing. it was the best FFT explanation I ever came across . This is probably one of the best visualisations of FFTs that I've come across

[@santiagooliveros901]

Facts man. I’m bioengineer planning to study my master in digital signal and image processing, and back to my bachelor days, the FFT was one of the biggest references we had to analyse the signals such as ECG, EMG and image from Fourier spectrum. So impressive the amount of applications we find with these algorithms. Edit: Also shout out to Veritasium for this amazing explanation of the FFT.

[@sarthaksingh2852]

@@santiagooliveros901 exactly..... and more complex or sensitive the data becomes with the help of FFT we could do far better analysis of data And like this kind of visualisation helps us explore a particular theorem or idea could be implemented at various places where we might generally not implement them

[@cedricvillani8502]

Learn about Spring and Spring Dampener Algorithms

[@leonponce8437]

same

[@HalitZiyaKARTAL]

which country

[@ghpkhg]

Another phenomenal video. As a teacher, your ability to convey this super-high-level information is impressive and encouraging.

[@isaackanu15]

Can you teach me this please

[@tetum849]

@@isaackanu15what? lol

[@dijoxx]

You mean low level?

[@aleskerovw]

I currently study signal processing at university and without this video I could've never imagined that the fourier transform was such a big deal. It's really sad how colleges don't take time to explain the importance of the taught topics before starting to lecture students on them. Thank you very much for making me see the big picture and realize how important are my current classes. This is the best kind of motivation to keep going.

[@crackedemerald4930]

I don't think a lot of people would appreciate having part of their precious expensive class time with a teacher taken up by a history lesson instead of the subject they're supposed to be teaching.

[@BrotherCheng]

@@crackedemerald4930 Properly motivating a topic is a pretty crucial part of good teaching though. It piques curiosity and engagement, and helps to anchor what you are actually teaching. I definitely think a lot of times university lecturers could just default into immediately jumping into a complex topic without properly motivating to the student why they should even care about it to begin with. Doesn't have to be a 20 minute history lecture, but just spending a little bit of time could go a long way. But honestly though, a lot of the technical how's and what's can be obtained through books anyway. The job of a lecturer is to teach, not just to regurgitate what the books says.

[@AXBA92]

Right? Most lectures are just like reading a list of definitions and formulas to memorize and that's it, completely voiding the subject of any context, relevance and usage. Good teaching is extremely rare.

[@sullivan3503]

@@crackedemerald4930 Wrong. That is a massively important part of the lecture, and typically the least boring part.

[@das250250]

Welch me to the University of KZbin where the best minds teach and express their curiosity .

[@SlightyLessEvolved]

This was, quite impressively, a much more clear explanation of how Fourier series & transforms work than I ever got in school.

[@dezmodium]

The Fourier discussion was deep and well explained but the discussion on the antagonisms between the USSR and USA here is really shallow and short. Both sides did have people attending these conferences who legitimately wanted to contain nuclear weapons. After all, they were mostly academics and scientists. But back home both sides had to contend with the political sphere: the senators and representatives that make up the government. These political actors on each side were not as thoughtful and were driven by fear and distrust. So even had the multiple talks about nuclear containment and non-armament ended well I doubt either side would have honored them. In the USA we had senators were absolutely certain the Soviets were planning world domination and in the USSR members of the Supreme Soviet (their senate) were absolutely certain of the same. Also it was a commonly held belief among many Soviet politicians that the Americans were literally insane and ready to use nukes at any moment.

[@KafshakTashtak]

If only professors did that before just throwing equations on board.

[@CuteLethalPuppy]

@@dezmodium yeah. Neither the USSR nor the USA were even willing to adopt the "No first use" policy. So I find it very hard to believe that the USSR, USA, etc would have stopped the nuke arms race if the FFT was discovered earlier etc etc. And I agree the Americans were and are insane in terms of nuke usage management - compare the USSR's Perimeter/Dead Hand with the USA's "The US President can launch nukes even if he goes crazy and nobody is supposed stop him" system. Search for "Harold Hering and the forbidden question that cost him his career."

[@Max_Jacoby]

What kind of school are you talking about? I graduated university with mathematic degree and we didn't study Fourier transform.

[@exazebra]

@@Max_Jacoby Any kind of school where you learn about signal processing. Digital electronics is where I learned about it.

[@response2u]

I study neuroimaging with MEG, and for signal processing, FFTs are very critical. I came across your video by chance and it was a supreme way of visualizing it! Kudos to you sir! The best explanation of the FFT for sure!

[@vikasrajyadav5915]

3blue1brown

[@suhcheuy268]

Same with me for EEG!

[@Bilangumus]

3blue1brown

[@jonrjd912]

I used the FFT in graduate work in 1974. We collected 1000data points from an average evoked potential from the spinal cord of a cat. The work was aimed at detecting injuries at different levels of the spinal cord using statistical (stepwise discriminant) analysis. We didn't have enough cats. If I remember correctly, the transform I used took less than a minute for 1000 data points from a 300 msec signal.

[@konstantinosvasios3852]

I studied Electrical & Computer Engineering. Needless to say Fourier Transform was our bread and butter. It is such a pity that usually the historical context is missing in the educational process. It helps so much put things into perspective and get a sense of the purpose and the significance of what you are being taught. I know so many students that are getting discouraged and disappointed just because the educational process only involves sterile mathematics brutally being thrown into your face without any context whatsoever.

[@muraliavarma]

Agreed! I always think that it is important to teach/learn things in a chronological order so that we actually understand the reasons for why a certain thing was discovered.

[@SmokeyVlogs]

i quit btech just because they sucked at teaching me mathematics effectively the professor was so rude he never answered my curious questions :(

[@nitesy381]

as a computer science student, seeing the letter n gives me nightmares. then when he starts visually showing the proof of how divide and conquer is time complexity nlogn around 18:00 makes me cry in C .

[@nitesy381]

@@SmokeyVlogs my heart goes out to you. professors like that are just the worst.

[@SmokeyVlogs]

@@nitesy381 much love dude

[@dakotahrivers6640]

As a senior electrical engineering student in college, i can say this is absolutely the most accessible and well explained video of the Fourier series/transform i've ever seen.

[@jcklsldr]

I wish I'd had it during my EE college days too

[@darrellhambley7245]

Long before Excel and MathCad we EE students did homework assignments using only a pencil and hand-held calculator to learn about DFT and FFTs. This video woke up a few thousand neurons which still had a whisper of that info after 50 years.

[@dakotahrivers6640]

@@darrellhambley7245 I have no idea how you guys did it. Whenever I’m doing homework I’m glued to my computer looking up how to do it and how it works. I seriously commend your generation of engineers

[@jcklsldr]

@@darrellhambley7245 I graduated in 2019 and never used Excel or even know what MathCad is lol we had to do everything by hand with hand-held calculators. The only time we were allowed to use anything else was for EM lab

[@takudzwandhlovu3013]

Spot on

[@ashishsrivastav6154]

During my Electronics Engineering course, we used to call it "Four-Year Transformation" as this was one algorithm that would stay with you for the entire four years and all signal processing calculations would need them (along with Laplace Transform)

[@murdo601]

These newer half an hour documentaries you are doing are just amazing!!!! What a high level of production for the rest of this platform to strive for!

[@Laando_]

Scrolling through the comments I realize that my feelings toward this video as someone who is currently a graduate student in Electrical Engineering is not unique at all. It's amazing what great animation and very well articulated and easy to understand words can do when trying to understand a complicated subject. I've taken probably 6 or so courses at least that use the Fourier Transform, along with classes that utilize the FFT, and never once fully understood what the hell I was really doing and why it worked. Thank you very much Veritasium, this has genuinely helped my understanding of FTs 5 years deep into my college education lol.

[@frotoe9289]

There's a lot of "shut up and compute" in some courses. Taking an advanced math class where the prof was covering Bessel functions (in gory detail for like 3 weeks) someone finally asked "ok, Dr Smith, we've spent 3 weeks studying these, what are they good for?" and the prof replied "I dunno--engineers use them for something, I think". Didn't know, didn't care. It was kinda comical taking an applied math class from a person who really had no idea how to apply the math--guess that was left as an exercise for the reader. One EE grad class the prof (guy who co-invented the Discrete Cosine Transform) decided we really all needed to learn to derive the FFT algorithm and do it on a test. And then a couple weeks later, decided we needed to be able to derive on the next test how to use DFT's to perform a DCT. Did that help us understand this stuff? Heavens no. It just forced us to rote memorize some magical math. But through reading enough stuff outside the textbooks, I finally (sorta) came to have an innate understanding. And yeah, well-done videos can go a long way toward providing that mapping from pure math to logical understanding of the concepts.

[@_NoName0]

@@frotoe9289 Yes, there's really too much of that, that's frustrating.

[@shoemakerleve9]

Painful stuff... Differential equations was enough for me during my time as a computer engineering undergrad. Will I use diffEQ again? Probably not. Did it make me have a deeper sense of understanding and appreciation of mathematics? Yeah sure I guess.

[@dadthelad]

Yeah this vid would defo have helped me understand Fourier Transforms quicker when I was trying to grok what the hell they were about in my undergrad electrical engineering degree. I did finally get it though, and then it was a glorious light of wow, how epic is this stuff!

[@6612770]

I highly recommend the following book for an excellent pictorial, intuitive and 'gentle' mathematical introduction to the basics of the FFT. The copy I have is: Title : The Fast Fourier Transform Auth: Brigham, E. Oran ISBN: 0-13-307496-X Pub: 1974 by Prentice-Hall Inc.

[@autom7134]

I love how you include all the historical context in your videos. It makes the already awesome explanation of an interesting topic that much better. Kudos.

[@jadams5240]

As a Electrical Engineering student who has taken digital signal processing, this is a beautiful high level understanding of fft. Love your videos man!

[@MrAnderson31]

As another electrical engineering student, I couldn't agree more. It's beautiful in ways I can't describe

[@t3chb0y67]

@@MrAnderson31 as another electrical engineer, I am akin to Nikola Tesla so if you have any questions just ask me

[@lidular]

Damn it. That was word for word the same comment I was about to write

[@dustinavant2003]

Good time memories staying up until 2AM doing FFT and Laplace.

[@niagara1238]

Ah signals and systems, memories.

[@garydunken7934]

Man.. the education system was so bad for me when I did my Electrical & Electronics degree at uni 25 years ago. I struggled to grasp the purpose and concept of Fourier Transform and subsequent lectures on DFT. Now looking at your visuals and explanation with historical relevance, it looks simply amazing and makes so much sense. Awesome work Derek.

[@RobbieK10]

I had the same feeling when I studied electrical engineering. The lecturers managed to suck all enthusiasm out of the subject.

[@pentachronic]

Same. However it wasn’t that well understood 25 years ago and was only kept in the hands of the top level researchers. More people have now digested it to make it easier to understand. Also we have the internet to get access to the people who can explain things properly and unambiguously.

[@hgff69]

@@RobbieK10 our lecturer gave this topic of FFT for self-study when there were no online videos and free course ware.

[@astronemir]

Engineering sometimes focuses a bit too much on application. I know it doesn’t make sense to teach every math proof but a bit of conceptual understanding of underlying algorithms would be hugely beneficial

[@don_marcel]

Bahahahaha that's why I switched to CS where we just talk about probability and number theory, but don't do actual math

[@youssefamrkadry]

I'm going to have to stop here and say this is the single most catchy, fun to watch, visually illustrative and informative FFT video I have seen, I wish I had a video like this 3 years ago it would've really helped. You're making a real difference here with videos like this and I hope you keep up the great work.

[@jonathan199224]

I literally named my dog Fourier because of the Fourier transform! My girlfriend's family never liked it and kept on calling him Simon for some reason

[@adamplace1414]

I've said it before, but watching Veritasium gives me the same mind-expanding wonder that James Burke's show Connections did when I was a kid. Not that this channel is copying their format - but just showing the intersection of history, science, and technology in a way that allows each to inform the others. It's such a useful way of teaching those subjects, and I'm genuinely happy there's someone still doing so.

[@mikestone6078]

I know exactly what you mean and feel the same way. It's something else to watch these videos. So much thinking that wants to be done afterwards.

[@PTRMAN]

I loved James Burke!! Even bought the DVD set of "The Day The Universe Changed"!

[@geoffstrickler]

That’s high praise…and I agree, many of the videos here have a similar feel.

[@akanhakan]

This is interesting. I cannot understand what people find in the Connections. I watched an episode a few years ago which was a complete disappointment. I thought it was filled with absurd just-so-stories to create far fetched connections packaged as knowledge/science. It was really embarrassing.

[@geoffstrickler]

@@akanhakan You’re probably viewing it with current production quality standards, not viewing it in the context of 80’s production quality and low BBC budgets. Check out his second series “The Day The Universe Changed”

[@EngRMP]

As a 66yo electrical engineer... it took me the last 20 years to finally understand the FFT as well as you've described it here. I recently realized that unfortunately the colleges do a horrible job teaching this subject... and I agree that it's one of the most important topics of math for anyone going into physics or engineering. I put together a radar 2D imager (ISAR) but using acoustics to keep the cost down. For the last 2 years I've been trying to get my local high schools interested in starting an after school geek club to teach kids basic signal processing using this acoustic imaging application. So far... no one is willing to even talk to me. It's too bad. Maybe your video will help. I really think that with the right application (acoustic imaging) this subject can be taught to 11th and 12th graders (multiplying sinusoids is really all you need to understand). This would prepare high schoolers beautifully for college science/engineering.

[@bluetorch13]

If you want reach, creating a short well made video and post it on all social media will help you a lot! its not hard.

[@EngRMP]

@@bluetorch13 Yup, I've thought about that. I'm not sure how to approach it... I have 100+ slides of discussion/description... probably 10 different applications that show the LFM pulse in slow motion so you can hear it, simulation showing the xmit to rcv correlation, simulation of forward and inverse FFT, sine cosine for phase angle, noise reduction through FFT size, resolution vs bandwidth, etc.. Then I have the imager itself. I've thought about showing the imager but that will only hook you if you're already interested in understanding the math. Animations like Veritasium puts together are REALLY difficult to do. His video is great... but let's face it... only us engineer/math geeks really followed his description.. it was great... but the non-geek probably did not really grasp the "area under the curve" or "sine vs cosine gives the phase angle", or the Euler expression. It's a tough subject to convey, or get someone interested enough to commit time. The beauty is that in an hour I think I can totally hook high school kids by showing the imager, then a brief discussion of why the xmit pulse looks like it does, then a simulation showing what happens when you correlate the xmit with the rcv from one, then more than one scatterer, and finally the magic of the FT that is basically a correlation with multiple frequencies.... and imaging can be described using range and velocity for a rotating target (ISAR).

[@happyfreeky]

I learned the basics in college then researched on my own. What helped was writing code and running tests for both audio and images

[@bradhayes8294]

Great idea from a mechanical engineer.

[@abraarsameer9521]

@@EngRMP You could do a van Biezen or Brian Douglas type video series.

[@primingdotdev]

Love the fourier decomposition explanation. Nice work.

[@jonpatchmodular]

Darn... I went in wanting to know more about how an audio equalizer and spectrum visualizer worked... I wasn't expecting to learn about nuclear weapons and cold war politics. This was an impressively good video, as usual! Yours has to be one of the best science dissemination resources out there for sure. Thank you!

[@masterjaques4440]

Derek's ability to break down mathematical terms into common language is amazing. As an Electrical engineer who works in Signal processing, the FFT algorithm is my bread and butter.

[@mth469]

What do you use FFT for in engineering, sir?

[@muhammadjunaid4948]

@@mth469 signal processing

[@feixin_duke]

pov you saw likes and felt insecure so you copied what little heck said

[@savagesarethebest7251]

Right, I have never heard a so succinct way to describe image compression

[@alanjones1581]

I had only been working for IBM about two years when the Cooley Tukey paper was published. At the time, we were working with a new computer language developed by IBM: APL. I was also working on problems involving signal processing so I implemented their FFT algorithm in APL. APL is based on arrays which made it a natural for implementing FFT. Even though APL was an interpretive language, the use of arrays made the routine very fast. The implementation only took about 20 lines of code. It was widely distributed within and outside of IBM when I published a non-confidential IBM technical report and presented a talk at an IEEE meeting in 1972.

[@AXBA92]

That must have been a once in a lifetime thrill. I'm envious.

[@alanjones1581]

@@AXBA92 Yes it was. I was at the right place at the right time. I had a fun career with IBM and another after I retired.

[@god0]

@@alanjones1581 did you know Larry Breed?

[@alanjones1581]

@@god0 Yes, I did. He was one of the key developers of APL at IBM Yorktown. How did you know him?

[@god0]

@@alanjones1581 I met him at Burning Man in 2004 and we were campmates until the pandemic. I went to his memorial last year.

[@divyanshrodney8322]

Really appreciate the time put into this video. Thank you for fueling my curiosity, makes me feel alive.

[@I_Santos_]

As a resident of southern Alberta, Canada, I am so thankful that the radiation fallout from all that American nuclear testing decided not to cross the border into Canada, as shown at 2:15 and formed a neat line along thr 49th parallel. 😅 Hats off to the CBSA for holding up the border like that.

[@dingding4898]

it wouldn't dare cross the border😏

[@hughdanaher2758]

The US tried to invade Canada 3 times and were repelled each time. What a border!

[@sorryplease5071]

There are a lot of engineers in the comments here, but I'm just a farmer with an insatiable sense of scientific curiosity. I can't thank you and some others enough for making this kind of information digestible for the common folk. The animation can't be cheap, but it's incredibly helpful for someone that better understands things visually. You have a powerful talent for teaching. Few things make my brain happier than understanding something as ingenious as the various topics you cover. It gives me goosebumps when thoughts and ideas connect together in understanding. I think it's called a braingasm and your work has given me many.

[@RedditFam]

yes sir! Derek does great job at explaining difficult concepts in such easy way

[@clonkex]

Out of curiosity, what kind of things do you grow?

[@toddeverson5699]

Just a farmer. You mean welder, electrician, mechanic, engineer, chemist, botanist, agronomist, economist, salesperson, carpenter, plumber, etc. Glad you still have time to be curious!

[@sorryplease5071]

@@clonkex Wheat, corn, soybeans, alfalfa, cattle. And it’s true that there are loads of adjacent skills needed to be good at it.

[@Lizlodude]

@@toddeverson5699 This is so true, farmers are freaking brilliant. SmarterEveryDay has a lot of great videos touching on all the stuff that a 'simple farmer' has to know and do on an almost daily basis.

[@adityashivaappalla1384]

FFT is the reason we are able to diagnose the problems with industrial machinery (pumps, compressors, turbines). As a mechanical engineer, I absolutely loved this explanation, but have to watch it again to understand it fully. Thanks, Derek for this work! 🙏

[@M1gu3L_Warzone]

CSI 2140

[@joebojanic1905]

Me too. I do vibration analysis on dyno systems and auxiliary equipment. I also worked in the cable industry and very lightly used it in signal analysis for troubleshooting.

[@sophiacristina]

FFT is used a lot in signal processing... 🥰

[@SquirrelTheorist]

That makes sense! I wouldn't have guessed but now that you mention it I see how they could apply in say motion detection software to that tests the durability of machinery (forgot the name but there's a video on that)

[@eduardoschneider2010]

you just made an amazing video. out of a difficult topic, you managed to explain it in a simple way. congrats

[@tonyt9697]

I think my lowest grade in college was in my linear systems and signal processing course. I felt such a lack of confidence in my understanding from that course that I took another elective on similar subject matter so I could better grasp the material. I wish I'd had this video back then lol. I really like how your video interleaves historical context alongside the theory - great video!

[@26paulifer]

Taking a complex problem, and decomposing it into the history, science and specific use cases is refreshing to see and should be explored more often in STEM education. Thanks Derek, and the team!

[@philkarn1761]

Taking something complex and decomposing it into a bunch of simple things...sounds like the FFT!

[@chaosjoerg9811]

Don't put history on the test, plz.

[@curween9009]

I was taught this, as I'm sure many engineers were, during University. However, its significance and real world usage was never explained, and therefore meant the work felt arbitrary, especially when performed by hand. This video explains FFTs in the most picturesque and simple way that I have ever witnessed it's amazing

[@rayaqin]

same We were thaught about this at the University but it felt boring and pointless

[@MJLNRGames]

Same here. I wish I would have been taught the history so I would have appreciated them more instead of hating them haha

[@Growlizing]

Holy hell yes. I spent so many hours doing FT by hand, and I did not even in the slightest understand why it worked.

[@shoemakerleve9]

Honestly university needs to take a better approach at mathematics courses. Having students wrote memorize complex algorithms and math models/approaches with no visualization is why math is considered so difficult imo. We need more professors like Derek (veritasium) in our universities.

[@jackallread]

Great episode! I did a lot of vibration analysis while working at a national lab and the visual explanation of the FFT was great and gave me much more depth of understanding! Often you can see how a formula is useful but now understand it and this helped a lot understanding FFTs! Thanks

[@imrannajir9332]

We had finished the FFT in just few days without knowing the impact and use of FFT. Story behind the FFT is really a treasure for a communication engeneering student like me Thank You for this amazing video.

[@ritwikism]

What an amazing video, I'm blown by the combination of storytelling, breakdown of complex math, connect to real life applications and of course the drama. This is top tier content.

[@pathagas]

i’m a math student, and i’ve spent a lot of time learning about/working with fourier analysis. i’ve really struggled to explain to people how important it is. this is a great video to encapsulate everything that’s going on.

[@babagandu]

Cool story

[@iankrasnow5383]

I'm a materials science and engineering student. Fourier transforms come up in many different areas we need to be proficient, and yet we never have a class that really teaches what they are or how to solve them. I knew at a vague level what a Fourier transform was, but I didn't know what a DFT was (except obviously being for discrete values) or a FFT, despite learning about various types of equipment that use them. I literally learned more about fourier transforms from this Veritasium video than from 4 years of undergrad engineering.

[@Atlas92936]

I am now convinced all wars are wars of mathematics

[@fredwerza3478]

I wish they taught the importance of Fourier transforms in high school --- it's a math concept that has shaped the modern world

[@judopunch2672]

Your production quality and presentation organization are insane. I learn things from you, thanks for your hard work!

[@charliemoody7168]

Enjoyed the vid a lot - but it was the ad for your sponsor that got my subscription. It’s good to see people succeeding at what they want to do, bringing all their skills to bear on a worthy outcome

[@justinyang21114798]

Another reason to why I love FFT so much is that it also happens to help visualize sound waves in ways that better represent how humans hear sounds. FFT is literally everywhere in music and technology.

[@yitzakIr]

It also powers reverb, you just multiply two FFT’s together

[@Periwinkleaccount]

@@yitzakIr what’s the ‘ for?

[@yanicklajoie6237]

@@Periwinkleaccount Why is the "t" missing?

[@warpedspeed4517]

​@@yanicklajoie6237 🖖🤣

[@okuno54]

@@Periwinkleaccount Generally, in (prescriptivist) English, an apostrophe goes between an initialism/acronym and the plural suffix. Personally, I find that rule silly and (marginally) ambiguous, so I also don't the apostrophe, and I'm not the only one to drop it, either. Then again, the only reason I might keep apostrophe in English at all is because double contractions look fun! "you'd've" "hadn't've" &c

[@Tigrou7777]

A quick note for the last part: image compression algorithms usually divide the image into small tiles (e.g., 8x8 or 16x16 blocks) instead of trying to compress the entire image. Sine waves are by definition infinite, and taking small parts of the image allows you to focus on a specific part of the signal (instead of trying to compress it as a whole). For example, parts of the image that are blurred and out of focus will likely contain low frequencies and therefore achieve a high level of compression. Wavelets do not have this problem (they can efficiently compress an image without dividing it into small parts). The use of small fixed size blocks is also useful in many other ways: lower memory requirements, parallelism, easier hardware implementation, …

[@derrekvanee4567]

Math... Checks out? I dunno mega over done comment komrad da, you deserve pickles and extra vodka ration.

[@synchronos1]

Also the image compression algorithms usually handle the lightness channel (Y) separately from the chroma channels (Cb and Cr), and not do it on the RGB channels directly (which I believe that multi-colour transformed image was trying to represent). The added benefit of this is that you can just bluntly downsample the chroma channels by a factor of four (at least on high compression), and a human eye won't notice much, if anything, as our vision is way better in discerning brightness differences than chroma differences.

[@tristanwh9466]

@@synchronos1 He mentioned in the video that the color represents phase not image color so what he showed would be the process for a single channel

[@awesomegmg956]

I remember JPG uses DCT instead of FFT?

[@mihailmilev9909]

@@tristanwh9466 thanks for pointing it out. Now only for someone to respond cuz I have no idea what it means anyways lol

[@user-sr2qk4jm9f]

I've taken a liking to watching your videos. There's a special talent of knowing how to tell a story. My attention easily gravitates towards your explanation. Thank you, and please keep making these amazing videos!

[@linimie]

We use global atmospheric models for our work and thus we use the Fourier Transfrom to apply grid based data in a spectral space global model, or the other way around. This video is really a nice help to understand where it comes form and what it does!

[@ShannonJacobs0]

New theory: Supporting antisocial trolls and assorted pirates is so expensive for KZbin that they are desperate to ramp up the ads. Are you seeing more and especially offensive ads from KZbin? Maybe it's just me? And is it related to the surge in hate-filled comments from the trolls? But in any case, I want to know if it's because my surfing with good privacy practices has starved the beast, so their ad picker is befuddled, or if they know it's me and it's just targeted retaliation and harassment because I keep commenting in public about how EVIL the google has become. The gun ads and racist t-shirts ads are especially effective at being annoying, but not at selling. If I ever notice myself shopping from a google advertiser, then I plan to stop it. And if you see this comment after many KZbin videos, that's because I saw another offensive and irrelevant ad.

[@FireAngelOfLondon]

@@ShannonJacobs0 Ad-block plug-ins are available for most of the major browsers. They naturally cannot stop ads incorporated into the videos but they can block the rest of them. And don't feel guilty about using one; you have the right to determine what you watch and what you don't and if companies make their advertising obnoxious they are pushing users in the direction of ad-blocking. I would prefer that KZbin get advertising revenue so they can continue to fund this free service and in that spirit I used to tolerate the ads. But as they became more objectionable I inevitably went to an ad-blocker and I have not seen an ad on KZbin in just over two years. KZbin's management are bringing this on themselves.

[@jordan9604]

I couldn't stand ads, that is why I use revanced and microg. Very effective and it even skips self promotion and other various things that you can customize. I know this sounds like an ad to get rid of ads, but I promise I am not affiliated in any way with those companies.

[@unbearifiedbear1885]

​@@ShannonJacobs0 racist t-shirts?

[@mercismerc]

I appreciate you used the same color scheme and font as @3blue1brown for this video. A nice way to pay tribute to their explanation of Fourier Transforms.

[@tomburnett3247]

Thank you this was a excellent description of FFTs. I’m 73 now and my PhD is in theoretical atomic physics. After school I worked for awhile with seismic data processing and we used FFTs extensively in acoustic scattering. This is the best explanation I’ve seen so far.

[@Ghxlib]

Do you regret anything in your life

[@razgvozd]

The outside is always regretable in any age. Even Christ regrets humans.

[@matthewthenerd792]

Oh thats intresting work. I've been working with acoustic sensors and FFTs for a while now; I'm with you in saying this is really a great explanation of FFTs.

[@NOOBCRASTINATOR69]

I wish I knew you in my life🌿

[@tim40gabby25]

Checkout 3b1b on the subject?

[@elliottwarkus8643]

I still remember when I first learned about Fourier Transforms in college. I was a music theory major who ended up switching to computer science part way through, and coming across something that so elegantly linked those two fields was beyond eye-opening. It was easily one of the coolest things I've ever learned about.

[@etiennepons4295]

I've just started a bachelor's in sound engineering, and having always loved physics and science in general, this video is amazing in showing how close music and physics are linked!

[@zohaibnadeem9385]

I'm not a music theory major but music is my passion and I'm studying electrical engineering going through exactly what you just described and it makes me so happy :D

[@pranavtagore]

Fourier transforms was the easiest stuff I could ever find in engineering maths.

[@level138inrs]

Im extremely grateful for this video. Ive worked with protein crystallography for years but really struggled to intrinsically grasp the FT concept. This video is the single best explanation ive seen. Will definitely be reccommending it to people

[@marcopozzo7886]

Derek, your videos are some of my absolute favorites, but this one blew my mind. Bookmark material! As a proud geek first, then an electronic engineer, I have dealt with signal spectra and their meaning since always. But how you broke down the complexity of the formula definition into its physical meaning, it's absolutely remarkable. Congrats on all of your other videos, too, and keep up this great work!

[@jcolinmizia9161]

I kind of love how literal the names of the conferences were. You knew exactly what they wanted to accomplish!

[@ShannonJacobs0]

New theory: Supporting antisocial trolls and assorted pirates is so expensive for KZbin that they are desperate to ramp up the ads. Are you seeing more and especially offensive ads from KZbin? Maybe it's just me? And is it related to the surge in hate-filled comments from the trolls? But in any case, I want to know if it's because my surfing with good privacy practices has starved the beast, so their ad picker is befuddled, or if they know it's me and it's just targeted retaliation and harassment because I keep commenting in public about how EVIL the google has become. The gun ads and racist t-shirts ads are especially effective at being annoying, but not at selling. If I ever notice myself shopping from a google advertiser, then I plan to stop it. And if you see this comment after many KZbin videos, that's because I saw another offensive and irrelevant ad.

[@unliving_ball_of_gas]

Sounds like the names you'd find in comic books

[@TheCangar]

As a neuroscientist using EEG I also use the FFT for basically everything I do. I did not know at all the background. Fascinating, thanks a lot for this video!

[@eduardogonzales6945]

Great content, I thought I knew about this topic, but there were a ton of things in this piece I had no idea about. Many thanks.

[@ateebahmed2237]

It is the simplest and most effective explanation of Fourier transform I have ever seen ! Kudos!

[@primenumberbuster404]

Fourier is one the most influential figure. As a math major when I learnt his contribution which leads to a whole bunch of mathematicians to make integration theory more rigorous and more powerful I was blown away.

[@neilsamuel5268]

You didn't even finish watching the video.

[@noname-codm4590]

@@neilsamuel5268 lol

[@primenumberbuster404]

@@neilsamuel5268 Well, I commented about Fourier and as a math major I know sufficient about FFT. You can easily check the description it's about FFT. You are typing this same comment everywhere. That's sad.

[@neilsamuel5268]

@@primenumberbuster404 As a computer science bachelor I also know about FFT but being on a laptop, it shows the total comments on the top of the comment section and it was already above 100 after 3 mins of posting... I commented the same comment everywhere because most of the comments seemed like bots as not many normal humans would comment before completing atleast 1/4th of the video. But FFT for the win! I hope you've seen the video of Fourier transformation by 3b1b! 🙌🏻

[@noob19087]

My deepest condolences for being a math major 🙏😞

[@mskellyrlv]

You've made some really great videos, but this is your masterpiece (I say that as a retired engineer who studies math and uses Maple recreationally). I knew of Garwin and Tuckey's contributions at the surface level, but the depth of your research was amazing (actually talking to Garwin was really cool). Even more astonishing was Gauss' discovery of the FFT. He is widely regarded as the greatest mathematician of all time, a title disputed by devotees of Euler. Gauss had an aversion to publishing his results until he considered them perfect, and above criticism: his personal motto was "Pauca sed matura", meaning "few, but ripe", describing his publishing habits. Euler, on the other hand, held a record on the number of publications of original mathematics unbroken until the late 20th century. I really appreciate Gauss' amazing contributions in all fields, but think that Euler outperformed him simply by putting forth more material that had never before been conceived. That's a digression, but it does speak to the question of "what if Gauss had published his result?"

[@philkarn1761]

I was pleasantly surprised to see that Garwin is still alive.

[@WanderTheNomad]

"Perfect is the enemy of good"

[@fredwerza3478]

Debating Gauss vs. Euler, now we're really getting into the academic weeds --- but I like where your head is at

[@michaelsotomayor5001]

In Spanish it translates “poco, pero maduro” or maybe the feminine version “poca, pero madura” but Spanish is my second language so I may be incorrect

[@chrisfuller1268]

The convolution integral and a radio receiver than scans the RF and IF simultaneously with narrow-band filters predate the FFT and could have been used but the scientific advisors had no practical knowledge, apparently. In fact, the narrowband filter is still superior to the FFT especially for detecting transient events.

[@arnsassassiner]

im an electrical engineer in my last semester . This is the best visual explanation of FFT . we use this a lot in signal processing .

[@Easi14h]

Yep, in my continuous time systems and signals class right now. It's a pretty big thing

[@jhjet510]

This is a SUPERB video. I’ve worked in Fourier space for over 40 years and this is one of the best explanations that I’ve seen. I was also unaware of a lot of the history as well. VERY well done!!

[@adamtaylor2142]

This is such high quality math/history content. Such a wonderful story. The history of the idea could fill a book, and it would be a rich and interesting one. You've captured its essence in 25 minutes.

[@teacup2301]

I did my dissertation on FFTs and I've been waiting for my favourite science communicators like you to cover it - so pleased with what a great job you've done with this video, as always

[@rudolphscheepers1200]

Note: The animation of 80,000 hours (number of dots) is incorrect, only 40 weeks is displayed instead of 50.

[@gururajgawanalli9971]

You really have a great impact;fan from India!You have to be one among the great explainers .With no background of waves or physics or even proper programming I was able to get the gist and essence of the FFT! Hats off;really continue making impact.

[@finneganmanthe8984]

5:05 Ah yes, the CESPDVPASNT. Truly one of the conferences of all time.

[@ElectroBOOM]

Love the video as always! 2:16 I'm just happy the nuclear fallouts stopped at the Canadian border, otherwise we could have had it bad here too! 😁

[@raj-m]

Wow! Electroboom

[@RAHULKUMAR-wn8po]

Animator stopped it.

[@lekhakaananta5864]

That's simply an artifact of the border. Upon landing on Canadian soil, the fallout particles said "sorry" and stopped emitting harmful radiation.

[@garydunken7934]

Stop knit picking Derek's video. Any appreciative comments this awesome video on FFT? I guess you still haven't recovered from the fallout with Derek after the 1/c problem video. LOL.. :)

[@revo1702]

Lmao

[@david.kirmayer]

I admire the depth of your analyses and how comprehensive you are making them. Thumbs up to 42Ve team

[@flwi]

Wow - that's truly impressive. I'm in awe by all the geniuses coming up with these algorithms that we take for granted. Thanks for the interesting explanation!

[@oh3991]

How brilliant was Gauss? He discovered a modern equivalent form of FFT in 1805, which is commonly known as Cooley-Tukey algorithm in 1965. This is 160 years ago. Even more crazy thing is that this also predates Joseph Fourier's publication of Fourier transform in 1822. He discovered this even before the Fourier transform is made.

[@aceman0000099]

If you think that's crazy, Pythagoras actually invented MP3 compression in 266BCE. Wild right?

[@pdcx]

@@aceman0000099 eli5. i tried to google search but to no avail.

[@Bjowolf2]

Fourier the plagierist 😂

[@user-ln2qr5mn8r]

@@pdcx its a joke haha

[@4321jirby]

Did this Gauss also invent the gaussian elimination I learned in linear algebra?

[@Banminator7]

It's pure genius how you managed to weave this storyline together with the very clear and understandable explanations so smoothly, you are a master at your craft Mr. Veritasium!

[@philkarn1761]

And he only touched the surface of the FFT's applications. I work in digital radio modulation and coding, and the list of applications of the FFT to modems and radio could fill a book. In fact, it does. *Many* books, actually.

[@brushstroke3733]

Clear and understandable? Is everyone who comments here a legitimate genius? I was pretty sharp in school, but this whole presentation flew over my head!

[@alexandrewashington6447]

I've said this before, but it bears repeating. This channel has two types of videos: great and excellent. This one in particular will be one of the unforgettable ones for anyone who watches it. Grateful for the attention.

[@RobMedellin]

For me it is just great which is high praise, but I like more many other videos. I think it's too deep a dive for many of us. Of course being too technical helps accentuate just how smart Gauss was, but Derek has made more impact in half the time in other videos.

[@tipilot3791]

this is my new fav video of yours. My jaw dropped when you mentioned Gauss lmao.

[@ManWithBeard1990]

A quick note on image compression: because of the n*log(n) complexity of the FFT it's common to divide the image up into smaller chunks. That's why on poorly compressed images or videos you tend to see blockiness. Now, what's interesting is that when you do that, instead of an FFT it often makes more sense to perform what's called a discrete cosine transform, or DCT, on those tiles. The reason for that is that in less detailed parts of the image, the most prominent components of a tile will be the average colour and an overall colour gradient. In a DCT, that information is mostly contained within the DC component and the first cosine coefficient, whereas in an FFT that information is more spread out. That's why DCT tends to compress a bit better in that scenario.

[@natec1]

So the blocks it divides it into aren't of uniform size? Are the chunks larger in less detailed parts of the image? If so, why does it appear to make parts of the image with little variation in color all one color? Shouldn't it be able to preserve that gradient? Or does it just throw that information out because it isn't very visually necessary?

[@Photosounder]

Complexity isn't the reason why blocks are used, blocks are used because there would be little sense in trying to compress a full-image DCT. And the advantage in DCT is in the way the signal loops, it goes back and forth before repeating unlike the DFT which only repeats and thus creates a big jump in values when it jumps which would mess up the spectrum. Which makes you wonder why they don't use Chebyshev analysis instead of DCT.

[@meneldal]

@@natec1 Depends on the standard With JPEG and earlier, it was all fixed size. In recent standards, size is adaptative, but you can't put blocks anywhere either, they have to fit in like 64x64 larger blocks that can be subdivided or not. Most encoders will typically use large block sizes on parts where there's less detail because it is more efficient.

[@halweilbrenner9926]

OK No idea

[@zackeeu]

Well d’uh!

[@shan_singh]

Future education will be inspired by these creators. I am an electronics and communication engineer, no teacher ever taught fft like this. Not even close. This is beautiful

[@manjupriya6574]

precisely my thought

[@bishrarar3015]

This is a great explanation to get a grasp on the Fourier transform, but it would not be sufficient for an engineering student. This explanation (understandably) glosses over a lot of details that are important for engineering.

[@panner11]

@@bishrarar3015 Well of course, engineering courses take months. This is a 26 minute video. Getting a grasp is often the most important part because it provides motivation to dig deeper.

[@TheSuperBoyProject]

Do the needful sir

[@sachins5784]

I've never understood the practical use of DFTs until I watched this video.

[@drewcompston4096]

This is the most intuitive explanation of Fourier transforms I've ever seen. You're so right that Fourier transforms are everywhere: I use them daily in my work as an electrical engineer of course. Interesting backstory about Tukey I had no idea about!

[@ricardolandeo2023]

I wish I had these kind of content while I was studying. I still wonder many other things I had learned but I see no use in my career but now I still find fascinating , how this is (or was) applied in real life. Thank you for the video

[@CTBell-uy7ri]

As a filmmaker, I’ve always been fascinated by video compression such as h.264 and h.265. The FFT is one part of those codecs that I could never get my head around. This video made it clear. Thanks Derek

[@adamrak7560]

I was a bit sad that he did not mentioned that the FFT in h.264 is not a classical FFT but a newer version, which is very significantly easier to implement in hardware. (some places call it HCT) (h.265 may be the same, but I have only read and implemented the h.264 standard)

[@CTBell-uy7ri]

@@adamrak7560 Cool!

[@pynchon9]

@@adamrak7560 DCT - discrete cosine transform.

[@adamrak7560]

@@pynchon9 it is not an FFT of DCT, as I have written the coefficients are wrong, that is why some documents call it HCT. (it approximates DCT, but there are some significant differences, so you cannot pair an exact inverse DCT with HCT, the results would be wrong) In practice DCT name is used for FFT of real even-symmetrical inputs, nobody actually computes the cosine transform. FFT is much faster and can do the same with the right boundary conditions as DCT.

[@TimothyLim-Roguengineer]

I studied Electrical Engineering, with an innate ability to understand complex math. I have used FFT for 30 yrs, yet seem to lack the ability to transform the concept into words for my family and other laypersons without their eyes glazing over in a minute or less. I am in awe of the rare, talented few like you, that seem to do both. With much excitement, I am going to force my family to watch this with me, and see if they can finally understand! YAY!!!

[@user-qy6tu9ip9v]

I dream of becoming a software engineer or electrical engineer but I don't feel that I am smart enough to understand fourier transforms.

[@kishoreytc]

🙏🙏🙏 thank you so much, no words, only respect for you brother.

[@pramod11925]

@@user-qy6tu9ip9v Hey it's something we discovered and you can be a teacher in it too always be positive ✌🏼☺️

[@bluex610]

@@user-qy6tu9ip9v don't worry, if Trump and Biden can be president, I think you'll be OK. Believe in yourself 😄

[@nicholashowie2829]

@@user-qy6tu9ip9v I know how you feel. I want to go into physics, but the subject is hard. The truth is though, if it were easy, we wouldn’t be interested in it. We can do it. It may take time, and a little more effort than some of our peers, but we can still get there. We will appreciate it more because we had to fight for it too.

[@AugustinHadelichViolin]

you do have a way for making very complex material accessible to laypersons. Content like this will go a long way towards making specialized knowledge accessible to everyone, so it will never be lost again. It's just silly that something this complicated yet revolutionary had to be figured out twice in human history.

[@juanrossi3]

Thanks a lot for this incredible video, man, great information, I like your way of explaining de FT, and the video production is great too, looks like a lot of hours of work. This is positive impact :)

[@SilverTear333]

When I first learned about the fourier transform it literally blew my mind. The fact that you can decompose any signal/function into frequency components fascinated me, especially once you see the value in real life applications. So much so that I now consider myself to have a life before and after I became aware of FT.

[@stachowi]

read the book "Pixel: a biography" amazing book....

[@Stierenkloot]

Doesn’t it make a lot of sense though? And our ears do this as well? We can tell different frequencies from a single speaker source

[@karozans]

I was amazed when I saw that you could use a Fourier series to calculate pi.

[@ivanscottw]

Let's not forget the phase.. It is integral part of the signal.. The FT/FFT/DFT turns a signal function into an amplitude/phase over frequency complex function.

[@98danielray]

@@ivanscottw the word "component" already implies you quantify their contribution to the system

[@antonalexandrov4159]

I love how you have such a wide audience and still are not afraid to delve into the more complicated depths of the topic. I am a little biased, since I have seen most of these things in my computer science degree but I believe this was one of the best ways to explain DFFT. At this point your video and 3Blue1Brown's video are the best way to learn the basis of FFT and get a really good intuition about it, not just a memorization of integrals.

[@dangerfly]

Is there a recent departure from simplifying concepts even further for maximum intuition or is it just these concepts are irreducible?

[@antonalexandrov4159]

@@dangerfly In general with content creators or specifically Veritasium? I wasn't really making a comparison with anything, I just haven't seen any huge channels like this that have content that for me seems requiring prior knowledge in maths, physics, etc. Which is why I felt that actually it's just his explanations being so good that even laypeople can get something interesting out of it.

[@fear7356]

As a high schooler, only some parts made sense to me, but his videos inspire me to delve deeper into these stuff

[@ToriKo_]

Have u seen the FFT video made by KZbin channel ‘Reducible’?

[@LuisSierra42]

Like PBS SpaceTime

[@bordershader]

Most of this went over my head, but I cancelled out with the bits that went under my head and managed to get a pretty decent signal out of it all. Thanks!

[@mohammadsharif9192]

I remember studying the fourier transform at college and having absolutely zero idea why we were studying it. This video made hate my college even more, cause it ruined a completely awesome subject on us

[@thebooduck]

It never seizes to impress me how you’re able to tell such a good story around a super dry topic like FFTs.

[@v44n7]

yet its the antique way of education that made it dry, you can check 3blue1brown videos and then you realize how wrong we learn stuff or at least, how outdated it is

[@ayushgupta-pc9yz]

Agreed! His narration is very good. But only an idiot could say that FFT is a super dry topic.

[@Ixs4i]

@@ayushgupta-pc9yz while i agree, for the average person any technical topic like this outside of common knowledge will appear dry without prior understanding of the subject, so i dont blame them for thinking its so hahaha

[@C.I...]

*ceases

[@Chris-oj7ro]

@@C.I... Bless you!

[@Cahangir]

Amazing video. Thank you for your efforts.

[@diptarshi1]

i can't explain in words the gratitude I owe to this channel. Explained to me FFT like no ever video in the world ever would. You are the GOAT.

[@simpaticode]

21:00 Gauss was a total badass. I hope someone went through those notes for more nuggets like this!

[@owencollier1071]

In my final year of college I took a class on Harmonic Analysis. This is a crazy difficult topic to make intuitive, and you've done a good job. Simplifying the problem by looking specifically at the terms of a discrete fourier transform and how they can be grouped is a great way of taking this complex problem and putting it into terms many people can understand. 👏👏

[@matttamal8332]

Yea not really. 3brown did it better

[@TasX]

Ikr? I’m also 4th year physics major and I never intuitively understood Fourier transforms and their algorithms until I watched this video. That’s insane how anyone would be able to figure out this orthogonality property from scratch

[@mrtoast244]

@@matttamal8332 i love 3brown1blue's video because of how concise it is, but this video did a better job in general for explaining the history of the fft and what context it's used in. It's also more entertaining compared to 3browns, which is mostly educational

[@fredrodriguez3913]

Why compare the 2 videos? They are both way more effective at introducing the concept than any previous pedagogical approach. I’m a EE and I learned something new from both

[@matttamal8332]

@@mrtoast244 Mm I agree with you that Veritasium is more entertaining. I figure the balance of jargon in this video is not to my taste. There are ways to explain this concept without it being a complex indepth math lesson. For those, I go to 3brown and pause and absorb the knowledge. Vids like Veritasium don't really flow well if I have to pause to understand since 50% of the vid is not as technical. You have to realize that this is only really okay for people who are pretty familiar with the field and these types of maths. Veritasium is a much more general educational channel, having to remember the rules of sines and cosines that I haven't used for years now is not really as enjoyable as the other half of the video. That said, I did brush up on it and rewatched it and the vid was more enjoyable, but that shouldn't be a prereq to understanding the beauty of the equation

[@ZVPieGuy]

I just love how "Fast Fourier Transform" sounds like a speed running strategy. Feels like I'm watching a Summoning Salt video and he just told us about a seemingly unbreakable time but someone just discovered a faster strat for the Fourier Transform level that cut several seconds off the run time.

[@tomo1168]

Another masterpiece from Veritasium. Please never stop making videos :)

[@robbechristiaens6384]

3blue1brown has a great video series about Fourier, greatly recommend to other viewers who are interested in this

[@gandalf8216]

FFT is how I got into programming of visualizations and plugins in for example Winamp, back in the day. Also hobby projects involving sound formats, from recording to playback. It's a glorious algorithm, which mathematically makes the bridge between a wave and it's quantization, something that's truly amazing if one thinks about it.

[@youtubeuser206]

so you're a gay

[@ypey1]

Oh my winamp! Does it stil excist? I made the titanium skin once

[@hl6816]

I first learned about FFT when I was adjusting the sampling rate and type of a de-noising plugin in a DAW. It's really amazing to see how it's shaped everything around us now.

[@MationGaming]

FFT got me into cyber security because I was so interested in using them to create quantumn-computer-resistant encryption algorithms

[@renaared]

It was when I discovered FFT that I knew I would someday get into DSP engineering

[@fr0styy202]

@Veritasium , fun fact. The footage at 2:22 was actually a ploy to scare enemies into the power of our bombs. This was discussed on the JRE. The single thing said to convey it was faked was “what about the camera?”

[@anthonykeller5120]

As someone with a BSCS I’m amazed that I never ran into this in any of the many math classes I took. It also never came up in any of the electronics courses or CS courses. Lots of calculus, statistics, group theory, and numerical analysis, but never heard of the FFT. I heard about from engineers later in my career, but never knew what it was. Thank you for a very lucid explanation.

[@magicalnoodles]

This is the best video about FFT and DFT I've seen thus far. Others have done similarly professional videos, but they are too focused on the theory. By showing the arms race, and then digging into the math and theory, you have masterfully shown us a practical and crucial application, before actually explaining it. I initially didn't have much of an impression on FFTs (even if i already learned about them), but after this video, it's very likely to stick with me for a long while. An amazing job indeed!

[@Stuen4y]

I wish this video was available when I was doing my computer science and electronics undergrad 10 years ago and struggling with understanding Signal Processing in my third year… great job as always.

[@theunheardprophet4315]

Someone called Ivanov was in the signal processing class in my third year of computer science and electronics undergrad but just a few years ago. Interesting coincidence nonetheless.

[@MikkoRantalainen]

My thoughts exactly! I remember listening a lecture about FFT during my university studies and the teacher could as well not be there because the way he tried to teach it provided zero value. If this video had existed then, I could have watched this video just once and understood in less than 20 minutes the whole thing.

[@vogelvogeltje]

Стоян Иванов?

[@philoso377]

Nice video and presentation. I take this video as the best in this channel. Learn the concept of FFT otherwise couldn’t myself alone. Thank you so much.

[@juan-fernandogomez-molina645]

great and simple, congratulations! Multiplication for sine/cosine functions, and analyzing areas according to sign laws is a more clear approach that using exponentials and complex numbers! FFT is the discrete-math version of FT, using finite intervals, windows and samples...windowing is key! Please do a video about windows in FT vs. wavelets!

[@trixgames1]

When I watch your videos I always feel like when I was a child that always wants to be a scientist, an astronaut, an archeologist, etc. The feeling of discovering things that will solve the questions in life. I always wait for your uploads just to feel like I'm a part of a group of scientist. Even tho when you are explaining the equations, I only understand a little of it but for some reason I completely understand the entirety of the topic. Thank you!