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.
Thanks for taking the time to write such a nice comment. Hopefully, you continue to learn more, there are quite a few great resources on the internet about Fourier Transforms and such (Better Explained has a pretty good one), and I think you'll find many more interesting perspectives and "aha" moments.
and you just wrote down my feelings in this comment, I'm %100 with you! I've been following people on RUclips and Twitter that are able to learn and teach in deeper and way more intuitive ways, definitely a better path for lifelong learning. Thank you both!
Zubzub343 I was about to right approximately the same comment ! I’m pursuing mathematical studies but it’s the first time in 5 years that I feel I’m getting a good understanding of the way this formula was contrived ! Really had to see it in motion, thank you for that !
5 Years ago, I said ... "I wish I had a brother like you, who could teach me so many complicated - interwoven stuff. Many people like me indebted to your wonderful contributions to the science of teaching" I just got my first payslip, and though it's not much. I am extremely thankful to you, for helping in my darkest times. For letting me know that there are passionate people out there, who enjoy explaining stuff. Though I didn't understand this particular video exactly the first time I watched it, the idea stuck with me, and one day after a few years, the same idea popped up as the most intuitive way of transforming a signal into it's "frequency" components. Then it all clicked and I watched this video again. Love your work ❤, I myself hope to explain some stuff that I am excited of.
You sir truly deserve an honorary doctorate - just for this video. Your impact to generations of confused engineering and math students will forever ripple through our society.
I totally agree, as a very young engineer math and physics had been thought in only repetition but not in the actual application and manipulation we can do with them. How we can play and control math is a topic i find really interesting and in which im very new at it.
It's crazy how Fourier was able to do this with just a piece of paper and his imagination, while I'm already struggling to follow this masterpiece of a visual explanation
And super computers at your disposal. Most people have little comprehension and appreciation for how important and inspired the giants whose shoulders we all stand upon are. The dedication and sacrifice our ancestors dedicated their entire lives to, is without parallel. The one thing they all had in common is a desire for fundamental truths. They were outcasts whose very existence challenged the staus quo. Just because we avoid conflict just to keep things copesthetic doesn't mean it is the proper path forward.
The guys bibliography is also insane. Born an orphan, became a mathematician, later traveled with napoleon and become a member of parliament. All while creating the groundwork for a lot of quantum physics. Guy lived one hell of a life.
@@wfps488 WHAT? damn, I feel bad about hating the guy when our professor was not even trying to explain the beauty behind fs and ft, I didn't understand them for shit back then, I wanna blame the prof but idk.
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.
Fourth year Physics/Mathematics student here and I've got to say first few times I did fourier transforms it was a nightmare and I really didn't know why I was doing it. But after just a few times I came to realise that they are much easier than people make out and so infinitely useful. So I wouldn't be put off of anything if it mentions that it has fourier transforms in it.
Yo dude, I'm in my 4th year at Manchester, hit me up with all the questions you want about undergrad physics. I can certainly remember how intimidating the whole thing is, so I would be honoured to do anything I can to help you along the path (I've just taken exams in GR, QFT [which is *all* Fourier Transforms basically] and Statistical Mechanics [also contains a massive amount of FTs], so hopefully I've picked up a few things you can make use of)
Came here to say the same: I studied in France and I too hated Fourier transforms... until I watched this video; I had no idea it was this elegant! Many thanks Mister 3B1B 🙂
I would say if you are confident on pure algebra and calculus, don’t worry about it. If you struggle with the concepts of what spaces you are transforming into, just don’t worry about it. That will come with time and experience. Just crack on with the maths. Worked for me, and I’m doing my PhD in spectral decomposition electromagnetism!
@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
Nobody is ever gonna read this, but i'm literaly mesmerized by the quality and accuracy of teaching this video posseses. It's nuts how well u explain such complicated things
Nope, we read it and we agree with you. I have 2 decades of constantly dealing with Fourier, Laplace, Smith chart, I came here for new perspectives. We live a revolution of teaching. Oh boy, I would have love to see this 20y ago.
I think you might be the best communicator on RUclips. 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!
I want to say one thing: Your skill in not only understanding and vocally explaining these concepts is so perfectly complemented by the animations you create that it blows all other resources on this topic out of the water. Even my college professors recommend this video specifically because, and I quote, "I could never create something so masterful that so aptly explains what is going on inside my head." Your skills are a gift to us all! I hope you always find as much passion in creating these videos as I do watching them.
It's incredible honestly, 3blue1brown and Sal Khan have made such massive impact; I might need to learn some chaos theory just to try to measure how we have profited as a species from just those 2. I would like to recognize educators in general for their hard work and passion, although, I think we can assess that a few individuals can be attributed a great deal of impact, similarly to say physics. There is a subset of a subset of individuals we can point at who we say have made great contributions, although if you point at them they almost certainly just point somewhere else; a giant standing on giant shoulders perhaps.
why is it that I spent tens of thousands of dollars on a engineering degree, and yet these videos do a much better job at teaching me what the math actually IS than any of my professors... Keep up the amazing work!
It's because even someone who has never taken pre-calc can see immediate applications to, say fluid dynamics, with inverse fourier transforms if fluid dynamics is something he/she is into. Those are the people that are likely going to use them in research roles or graduate school. Whereas vast majority won't ever touch them in a typical engineering job. It's like throwing out bait to hook one or two students a year.
Yeah, my main problem with my degree so far is they teach the pure math... not what it's for. Showing me equations upon equations does nothing for me without a base explanation of the usage. People say these videos don't touch on a proper university education, but without this video I had zero clue. Now I can actually understand the lectures and the math 😅
@@SakiDGit makes sense they try to make you understand the thing rather than each individual application. As an engineer, the ideal would be that you comprehend it enough to recognize the opportunity to apply it in whatever context it would be useful. However, for that you need a strong and intuitive(without gaps) comprehension of how the math ties to the real world and the comprehension of the Fourier transform nature on top of that. But that's very rare. In general, people really struggle with abstraction, and math's favorite toy is abstraction, to the point of abuse. I would say that abstraction is part of the core of math itself. But teaching people math this way is really difficult. Just as it is to teach anything without a bunch of gaps; a bunch of missing links of how things lead to one another. And its also inconvenient, for the system to test that and to basically turn you a basically a master of 10 or 20 subjects or areas. Managing learning is the toughest part of learning anything. The educative systems assures you a lower boundary for how bad is good enough. You get a better chance to get a much richer, faster and leaner learning by managing it yourself, but you also get the chance to screw it up badly; super slow progress or the absence of progress all together, much more and deeper misunderstandings, more gaps in your knowledge, etc. I don't have an engineer degree. Nor have I took classes for that, but I consider myself an engineer; for me being an engineer is to understand the nature of things and influence them towards getting what you want or the closest to that.
It’s not so much as to “discover” this stuff, but rather, using models and constructs to simplify the world around them in order to understand what was previously too hard to. These mathematicians were just so eager to see nature unravel in ways that unraveled cool secrets, that everything from calculus to Fourier transforms, etc. were built, rather, out of this curiosity.
The amount of clever someone has to have in order to explain it in such a simple way! At university my (very good and passionate Professor) took more than 1,5 hours!
I am a newb in the regard of creating math, but I would assume it has more to do with seeing enough relevant constructs and making a small or big leap based on alot of background. By no means do you need to be excessively clever to come up with this stuff, not even have a killer amazing amount of background. I just have come to believe that that's the case.
I know rite? Especially in math, physics and chemistry, sometimes I'm just sitting there wondering how on earth people managed to find this or that formula, or realize that there was this connection to that, which makes solving whatever problem 100 times easier. Something I still really don't understand is how astronomers figured out the orbital period, velocity and distance to earth of the different planets just by looking with their _eyes_. I also wonder how on earth Newton actually tested his equations of gravity to find out they were correct.
I'm speechless with this work of art. The explanation of the underlying principles is amazingly clever, and the visual production is outstanding. I can't imagine the amount of hours needed to make all of this. It's an honor to have watched your video!
I study Applied Mathematics and I think of myself as of someone knowing quite a bit of mathematics and also (from what others say) having some sort of skills in transferring this knowledge in a pretty understandable way to other people. But compared to you... Well - YOU ARE SIMPLY A DIDACTIC GENIUS! The whole 'scenario' of each episode, the way you move from the things which are very easy towards the more difficult ones, the examples that you pick, the interpretations that you find, the visualizations... Each video is just a mathematical masterpiece! Thank God there was a moment in your life when you thought that your mission is to show the people the beauty of maths on RUclips. I cannot think of anyone doing it as good, as you do. :)
I am an electrical engineer and I studied Fourier Transforms in university and remember not understanding how it works. In my job I actually use Fourier Transforms to view the frequency domain, but again tools calculate it for me. When I viewed this video, it was the FIRST time in my life I finally understood how Fourier Transforms work! I absolutely love this video! Awesome job!
I'm a retired neuroscientist and now a part-time middle school teacher. I teach digital music production, and I rely heavily on Audacity software in my class. The noise reduction algorithm relies on Fourier transforms (which I have never understood adequately), and this video has helped tremendously! Thank you so much! What an intelligent way to reduce unwanted noise! Far better than a simple noise gate. Nice to finally understand the way it works. Sorta...
@@ahreurink In my research, I never used EEG readings. I know they do use a complex noise reduction algorithm, and I'll bet it is the fourier transform. My work involved more of the molecular biology and behavior, and my labs mostly used animal models. Getting an EEG reading on a poor little mouse is not easy.
@@ahreurink Wow, neuroscientist to digital music middle school teacher is not a career path I would’ve guessed! Your interests and skills must be very diverse.
I've been an engineer for over ten years (my roommate was the signals junkie and I was the embedded systems dude) and you are the first person to actually make me understand the derivation behind this thing.
15 years ago I was a chemistry student and I had to take exams on linear algebra and calculus. And I specialized in spectroscopy. That was a long time ago, now I'm in another sphere - computers, and I've forgotten a lot of details, though not the basic concepts. Let's just say, your videos made me connect a lot of dots in my mind. Incredible work, man. See, it did happen for me to teach - there was a schoolgirl next door, whom I sometimes helped with the lessons. Once she told me that she gets higher grades if I explain the lesson to her and that I was born for a teacher. Yet it's guys like you, that I take my lessons from.
I can relate to that feeling too, but to be fair, it probably finally sunk in because you had built notions and worked with them before despite not understanding them to this level of intuition
About 8 years ago, YT had a 5 star ranking system. I preferred it a whole lot more.. However, that meant you couldn't save the video in a "liked" list unless you favourited it.
Mikky They got rid of the five star rating system because the vast majority of ratings were either one star or five stars. People are hesitant to give a "bad" (read: less than five stars) rating to anything that has no significant flaws, even it is fluff rather than solid content.
Thank you for this! I have a BS in engineering, an MS in Computer engineering and none of the math, or signal processing classes I've taken explained this in several semesters as clearly as you did a few minutes. It all makes sense now. I finally get it. Bravo! Standing Ovation!
It's hard to overstate how valuable your videos are. They breathe life to difficult concepts which are often just presented without any motivation/explanation and expected to be taken for granted.
Words cannot convey my gratitude to you with making these videos, you are helping so many people all around the world to see the beauty of math, for what it really is. Thank you. You taught me more than any of my Math teacher ever did.
This is not only helping many people to see the beauty of math. People who understand these concepts more intuitively become better engineers, physicists, software developers, ... Better teaching creates a better world. I wish there was a 3Blue1Brown for every field
I just came back to this video again after a year or so just to re-watch it because thanks algorithm, and I came down into the comments to make this exact same comment only to find this one. :D
@@SoftwareEngineer-A I'm not terribly well-versed in specific jazz artists/bands, unfortunately. I've just had a few years' worth of band experience in high school and subsequent music theory osmosis vis a vis Adam Neely more recently. ^^;
@@calyodelphi124 Coolio. Well, if I have but 1 album to recommend, it would be The Black Saint and the Sinner Lady as it 1. fits the description, and 2. across the 2000 albums of which I have listened to and logged, it stands as the most perfect representation of music that I have personally ever had the pleasure of listening to. :>
I've had 5 years of undergraduate/graduate maths education and this is the best introduction to Fourier Transforms I've ever seen. Amazing. I must've done a billion Fourier Transforms and I've never seen it explained in this way. Plus the fact that you were able to derive the integral definition in a way that I feel anyone willing to learn it will understand easily is incredible!!! Keep it up man 👌
I somehow managed to get a computer science degree without once learning about Fourier transforms (though I narrowly avoided them several times). I'm not sure how I did that. But watching this video, they make complete sense! So often, "complicated" math concepts are taught purely symbolically, but understanding *why* they work, from the ground up, is extremely important -- and, for me, it's the thing that makes math fun! I guarantee I won't remember the details of this in a few months unless I watch multiple times, but if I ever run into a need for Fourier transforms, I also guarantee I'll be thinking of this video to figure out what I need to do :) So thank you :)
IceMetalPunk Explain it to yourself a few times after watching the video a few times, then explain it to others so they also see the big picture. That is one of the best ways to learn it. 👍😊
This is the best intuitive description of the fourier transformation i've ever seen. I've used fourier transformation several times, but it always seemed like magic. This goes a long way to make me understand why it works. These visual ideas are so important - and they are much easier to understand in a video than by reading a description of them in text. Amazing video!
Every time you upload a video I think: "eh, I've studied that before and these are supposed to work as an introduction for an unfamiliar audience, I'll listen to it in the background or something". And then every time it's a mind blowing approach. When you say something like 14:43 and I realise where you're going with it I'm always surprised and amazed at how elegant and cool you've made the topic.
That's why mental laziness and complacency is always a potential threat to any of us, even more so when you think "oh, I've already learned that" in your head, or you go "oh, I can't ever be mentally lazy; I have a college education and studied hard." I've been guilty of the same in the past sometimes but I keep these ideas in mind and actively try to be better. Remember: you ALWAYS have something more to learn. NEVER stop trying to learn more every day (or at least improve/further clarify your current understanding on subjects at the very least.) Having worked or studied hard in the past is no reason to get complacent in the *present* and think you're "done" already (that's just "self-justified" laziness, in my view.) That's the attitude I try to take at least ;)
Dang - I stopped taking math in 10th grade after my AP Math teacher took me out of the program because I didn't like doing all the extra homework. After going to school for music but becoming a programmer, I continued to learn more advanced math as needed. I've had random times where I've used the Fourier transform, but never really understood it or why it worked. This made it crystal clear and it feels good to fully understand what is going on both conceptually and in the notation. Thanks a ton for your time putting this together.
I'm studying engineering and I've been passing exams like calculus and acoustics where the concept of Fourier Transform (and Laplace too) should be well understood. But nobody ever explained it clearly or tried to, they just gave us the formula for the series and that's it, we basically had to accept it blindly. Researching on my own just gave me back analytical processes to get to the final integral, but without explaining the meaning of each step and just putting even more confusion in my head. I also like to make music so I've been playing around with equalizers and the like for a long time and I ended making up my own idea of how the frequency analysis actually works. But now in just 20 minutes you managed to fill one of the biggest gaps in my knowledge and I'm so happy you made this video, like from 14:29 on I really started seeing rainbows all around lol. Thanks a lot for this vid, I can't wait for the next ones
Same experience as yours. I had to accept the transform without understanding what was the thinking process of M. Fourrier. Pretty sure he was teaching it that way, when alive. Upper grades in mathematics would be much more interresting with explanations like these. Professors are lost in the abstractions and have lost (or never had?) the art of transmitting the knowledge.
jshowa o maybe it's important to read a little bit of Shakespeare here and understand we are humans After going through that, i believe it's important to understand stuff for the future of humanity, don't you find it odd that math is taught so badly? And that people that studied math a couple hundred years ago not more were chased and burnt to death? Something's going on here. But even more practically: don't you think that when you understand stuff you just are faster and better doing everything?
I remember struggling through the maths of Fourier transforms at university, many decades ago and I've long since forgotten it all, but this video is a very intuitive explanation. I just wish we had had such graphical illustrations when I was trying to understand it.
I've been subscribed to you for a while now and have thoughts since the beginning that you have a very rare talent for explaining mathematical concepts but this video might well be the most awesome explanation of a mathematical concept I've ever seen. I've recently left academia after a PhD in Particle Physics so now I don't get nearly as many opportunities as I used to to get excited about Maths and Physics but every time I see that you've published a new video I get excited :-) And of course as many others here, I really hope that people will start using material like this in lecture theaters. It gives so much more of a sense of the beauty of mathematics than writing on a blackboard ever could...
I've been using FT's most of my working career (40+ years) and this is the most insightful and fascinating explanation of the FT that I've encountered. How I wish this stuff had been available in 1980!! Brilliant.
I love how you went through building up the expression that would later be the "fourier transform" function. It's been my thing to make sense of equations. They're not just variables that you can plug and chug. Each term in a formula stands for something that should exist in the real world, and knowing what it means just fills my heart. Keep on fighting the good fight, Grant
I DID NOT expect to get pretty close to understanding Euler's formula in this video. When I first saw that, I thought it was going to take me forever to understand it, but it just happened passively while trying to learn something else... This is an awesome video
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!!!!
7:07 I just realized the reason it's giving a big spike at the zero frequency. When you move the frequency graph up, you're basically adding in another wave with a frequency of 0. The fourier transform still works
Yep, good point, it's the "DC coefficient", as we would call it in the context of the Discrete Cosine Transform (similar in concept to the Fourier transform) that is at the heart of MPEG video compression (though I'm sure that term is used in other contexts as well). As opposed to the "AC coefficients". Borrowing terms from electronics.
Look into the Dirac delta function. It turns out that the fourier transform of a constant is the aforementioned function. Your realization is more profound than you realize!
@@victorwilburn8588 correct you want a pure DC waveform molecular Attenuation Field Density , AC hum " 60 Hz " Thus why in order to activate TRUE NMRFA of molecules you have to use Pure source of DC energy Alternating Current " Hum "contaminates a pure Sine wave frequency.. US War department R&D 1946 Infrasonic Waveform Weapons technology.
Honestly as a maths student in my 3rd of 4th year, watching your videos reignites my passion for it. Thank you, you're doing a genuine service to us all :)
It is unbelievable that there is such a simple explanation for the "thing" that the teacher has been teaching for months but left undefined! Congrats sir!
Your channel is LITERALLY more educative than all the universities in my country. Amazing. Your videos have seriously sparked my interest in mathematics.
I have a PhD in Engineering and I never had a teacher explaining Fourier transform so intuitively. We have been defrauded by the academic institutions. Also, I have not seen a textbook explain this concept so elegantly like you did. I want my money back!
I'm an astrophysics postdoc, so I've done my fair share of FTs over the years, but this is easily the best explanation of them I've ever seen! I finally understand why they look like that
This is precisely what i want everything to be taught, with visualization and intuition that touches the heart of the matter. I admire you greately, man. Gotta start learning that insane animating skill !!
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. :)
The best, simple, easiest, and valuable video I've ever seen on Fourier Transform! Of course I had learned it from the class ,as a university student, but the professor taught us literally based on 'the formulas', didn't have any idea of give them 'a life'. This channel did it and now I want to say thank you over a hundred times to those who contributed to this video!
Wow can't wait for the uncertainty principal!! I have to say you give me so much motivation for my studies (physics). I think without you my grades would be so much worse than they are now!
I'm just a musician wanting to understand more about sound...haven't done math since high school...this video was probably the first time I have enjoyed math...ever. Amazing stuff!
I have a master degree in Mechatronics. I had lectures in Signal and picture processing. I learned how the transformation behaves, its properties and what happens if you change the function, shift, strech it etc. But nobody gave us an analogy to understand the tranformation formular itself. Thx man. Now I have a new perspective to this topic.
I took a class on this in College and I still had no idea what Fourier Transforms were when I finished. The first 2 minutes and 22 seconds of this video made it abundantly clear. Well done! Clear, visual, best-in-class video explanations like this, that can be watched over and over again from the comfort of your home is a game changer and will disrupt the traditional and expensive College education system as we know it. I think Khan Academy is on the right track. If they start giving out degrees it's Game Over.
i think you are somewhat hiased. these types of explanation is mostly apreciated by people.who already got ass burnt by college courses and were forced to solve problems/projects/whatever your uni is up to, then forced to somehow "make the notions work for them". at THAT point those 3 minitues made your brain snap and say "that's it!" and probably lots of electronics, signal, automation notions came together (look at how similar are those patterns to equilobrium criteria in auyomation control). are we sure it will work the same the other way around? without that ass burning college part?
me too bro. understanding concept to the core is what i also seek, but tradional college is just a degree machine, where u gobble all formulas and vomit in paper. no idea what u studied in ur entire degree. i also love khan academy. :). do u know another channel or videos which can help great in college level math. like partial derivative,
I am literally speechless, I don't know how could I thank you for this stuff. I wish our teachers would have taught us in that fun way, where maths feels natural.
If I had had a chance to look at your vdo 30 years back during my electrical engineering classes, I would have fully grasped what I actually completely lost back then. My goodness, your explanation and graphich presentations are unmatched by anyone on this planet.
Funny how we pay loads of money to learn this stuff at university, yet we all still come running to free online video lectures because no professor can match them in terms of quality.
I was just thinking about how the reason I dislike this kind of RUclips channel is for the same reason I dislike other similar channels, such as Veritasium, Numberphile, SmarterEveryDay and VSauce. The trouble is, you aren't really learning anything. In University it usually takes a long time and you have to start from the foundations and work your way up through the rungs one by one until you arrive at the point where you can follow what you've learned into the workplace and do it professionally. This kind of channel uses the "wizzbang" or "wow" approach of endlessly cherry picking isolated curios and well known and popular but poorly understood ideas. In University after this you would be tested by having to produce maths or write programs which use what you've learned to show you can. You don't get that here and it's my guess almost nobody who watches this video goes on to actually sit down and write their own FFT. In the end, you just add it to your store of useless information.
@@vapourmile Actually, I got to disagree with you on that one. I think you misunderstand the goal these types of channels have in mind. They aren’t academically ‘rigorous’, because such long-winded video’s would only be watched by those already schooled in physics/mathematics. The aim is to help conceptualize idea’s and inspire people to investigate for themselves. The importance of communicating science to the general public is something that’s often overlooked. As for 3B1B, I actually did learn something from this video. My university did nothing to provide me with a good concept behind Fourier transforms. Basically, I was handed a 10 page document with all sorts of mathematical wizardry going on, so that by next lecture they could use Fourier theory. I might have kinda understood the derivations, but I missed any visual intuition as to why Fourier transforms worked. After watching this video I went back to that document and it made a lot more sense. I believe many people just end up memorising the formula’s, without much understanding. It’s a lot harder to find new applications for a theory if you don’t really understand where it comes from and what makes it work.
@@vapourmile I mostly agree with you here. The aim of the videos isn't to give a deep understanding, but to give the viewer a neat intuative sense of what's involved in the topic. However, I love these channels! It makes these difficult topics accessible for, well, anyone. And in my case, I often come to these sorts of channels to supplement my academic learning. I find lectures to be quite dry and difficult, but when I combine that rigorous understanding with this intuative understanding, that's when I'm most easily able to work with and exercise these ideas!
@@petermarsh4578 Exactly, people often think that this is all formal academic course teaches you and say "school and college bad!!!". Videos like these are meant to explain the bigger picture of a subject, not to replace rigorous academic study of it. At best, these are meant so that the general public understands more (not all) of the topic, and as a "companion" for those studying it in an academic institution.
i had some excellent professors, however it doesn't really matter too much if the professor is bad or not since learning math takes a ton of self study anyway. The people complaing about bad proffesors may have valid criticisms, but when you do research you're basically on your own and it doesn't really have much of an effect on your education, though all your colleagues will be massive math nerds.
I can watch it a hundred times and still not get tired of it. I can only imagine how difficult this would have been for me without this kind of explanation
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.
Perfect 5th, then minor 7th chord. a great start to a great video. it's insane to me that your ear and brain can do what a mathematician does on paper instinctively with a little practice, yet the same is true on paper still; furthermore, the math can take these concepts and turn them on their head and back again. By the end of this video, as expected (at this point in my experience with 3b1b), I am intrigued, astounded, and curious. I have felt tempted to give up on my passion in math recently, as I've taken up a strong interest in music, but I've been proven time and time again that the two work together, almost interchangeably. Thank you for taking the time to make these videos. Your talent in visually explaining intense mathematical concepts persists like none other. When is there going to be a series similar to your Calculus and Linear Algebra Series, but for Diff Eq and MultiVariable?? with love, a subscriber.
I have finished my Electro-technical university 22 years ago.... FT was one very important thing ... and only after 22 years , I really understood it ... THANK YOU FOR THIS VIDEO
taught you MORE than 2yrs of lectures COULDN'T teach you??? what 2 yrs of lectures COULDN'T teach you is almost infinite, so your statement becomes trivial. apparently X yrs of language and composition lectures likewise failed to teach you how to express yourself accurately and precisely. maybe you're just not college material. or maybe you need to learn to think FIRST and only speak afterward, rather than blurting out the first thing that pops into your head.
+Adam Nasir - if you think my comment to pranit was insulting or contained a put down, then YOU are an touchy-feely politically-correct IDIOT. see the difference? THAT is an insult (even tho conditionally true). i corrected a blatant LOGICAL error that had NOTHING to do with the commenter's native language, and everything to do with careless sloppy composition. sloppy speaking (or writing) is the surest barometer of sloppy thinking. also, don't you think pranit can defend himself if he felt the need? aren't YOU the one being condescending by ASSUMING that pranit needs you to butt in and defend his honor? how arrogant and presumptuous, not to mention passively-aggressively insulting to pranit. or are you too "logically challenged" to follow the implications of your post to their inescapable conclusions? dimwit.
John Michael You two are having a misunderstanding because judging from the type of answer you both decided to give... a) you made logical approach, focusing on the logic problem of the original post, whereas b) Adam Nasir interpreted pranit pawar's message a different way by guessing its intended meaning and perceived your message probably as quite blunt. Therefore - and this is my perspective and how I interpret the collision of you two - you two may be talking about the same topic but on two different levels. Whether or not this conversation makes sense is a whole different question, because we don't know how pranit actually meant his message to be understood. Was he being sarcastic? Was he having a bad day and he used this message to express his emotional situation? ...which btw isn't more than a tiny snapshot of what pranit really thought when he wrote this. Or are we thinking waaaaay too much about all this, because pranit just wanted to express that this video is genius because it explains a complex topic in so little time? If the topic is important to you it can help to ask the one who gave a statement, how he/she means it. That helps you understanding whether your thoughts are relevant. Or don't ask, speak your mind and prepare for conflict. ;-) Communication is a beast. 🤙🏼^^
Such videos should be on the beginning of every university class. Purely explained on animation. Finally i understand how it works after 10year of my university graduation.
I have no words to say how much impressed I am by this video. More than twenty years ago, at University, I was literally going crazy just trying to understand where those formulas were coming from and what they were trying to represent. I no longer have to know that, but still it was in my mind. So today, pushed by laziness and curiosity I've gone through this video, which relly blew my mind. Really a great job!
Brother, You deserve an applause, because of the Explanation and the Modeling of the video. I really appreciate your work, and all of us are thankfull to you, God bless you
I have Master degree of mechanical engineering and your videos helps me a lot truly understand math and physics. Thank you so much. Your brain is beautiful. Now I see that complex numbers nad FT it is just smart mathematical tool.
Absolutely, positively, the most stellar and intuitive introduction to Fourier transforms I have ever seen. You have far better explained, in just 20 minutes, what my uni lecturer ever could in a semester back in the day.
My favorite videos on this channel are the ones where I think I have a pretty good intuition on the topic already, but I still leave the video feeling like I learned something new. Fourier Transforms are ubiquitous in EE and I wish this resource existed when I took my first Signals and Systems course in undergrad.
As an electrical engineering graduate I SERIOUSLY wish this had come out while I was still in college, SUPER insightful and it all comes together and makes SO much more sense now. I always thought of it as a shorthand "switch" back and forth between frequency and time domain, but the polar graph and Euler's equation makes SO much more sense.
Josh Garber well, technically it IS a shorthand switch between freq & time domains, bc interpretation & manipulation are easier in one or the other domain, depending on the circumstances. But you're right; the explanation in this video is superb & goes beyond just freq & time domain.
If I ever become a professor, when the moment comes to teach Fourier Transform, I'll just put on this video and sit with the students. There is absolutely NO better way to explain this concept
@@StrawberryLegacy I like it when profs are looking a bit behind the edge and are actually giving you other good sources to learn other than their own script
This video helped me tremendously. I have only one complaint about this video: I had trouble figuring out exactly where the 'center of mass' was supposed to be because I wasn't sure if the mass-density of the wire wrapped around the circle was uniform, or whether it was the mass-density of the wire in Cartesian coordinates that was uniform, or both by somehow scaling the circle or wire to make it so. Only by the end of the video was it possible for me to deduce that its neither, and the mass-density is instead equal to the radius times the 'dt' infinitesimal of the unit-circle arc length. It took me 40 minutes instead of 20 minutes because I had to sort though my confusion first. But I don't care. I am extremely grateful for this video. It was awesome. I'm a physics-major and I never understood the Fourier transform until now because my university didn't go over it carefully enough and their continual torrent of homework assignments never allowed me to look into it independently, and yet, they required me to use the Fourier Transform after only giving me a highschool-level explanation of what it did, and this triggered my ADHD terribly because I need to know everything. I am extremely grateful to you Grant, and also a little annoyed at my University.
The world needs such videos to develop the right attitude and the mindset for the real learning. Amazing and hats off. We learned things in our schools not only in pretty boring way but also in the useless way that prohibited us to appreciate the beauty of nature.
![Felix "Unfair" | [Stray Kids : SKZ-PLAYER]](http://i.ytimg.com/vi/Oswujxm2Ag0/mqdefault.jpg)
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.
Thanks for taking the time to write such a nice comment. Hopefully, you continue to learn more, there are quite a few great resources on the internet about Fourier Transforms and such (Better Explained has a pretty good one), and I think you'll find many more interesting perspectives and "aha" moments.
and you just wrote down my feelings in this comment, I'm %100 with you! I've been following people on RUclips and Twitter that are able to learn and teach in deeper and way more intuitive ways, definitely a better path for lifelong learning. Thank you both!
Your comment resonates so much within me. I had never even come close to getting an acceptable intuition about these frequency transforms.
Your the reason i have an A in Calc AB. You make math so fun and interesting!
Zubzub343 I was about to right approximately the same comment ! I’m pursuing mathematical studies but it’s the first time in 5 years that I feel I’m getting a good understanding of the way this formula was contrived ! Really had to see it in motion, thank you for that !
5 Years ago, I said ...
"I wish I had a brother like you, who could teach me so many complicated - interwoven stuff.
Many people like me indebted to your wonderful contributions to the science of teaching"
I just got my first payslip, and though it's not much. I am extremely thankful to you, for helping in my darkest times.
For letting me know that there are passionate people out there, who enjoy explaining stuff.
Though I didn't understand this particular video exactly the first time I watched it, the idea stuck with me, and one day after a few years, the same idea popped up as the most intuitive way of transforming a signal into it's "frequency" components. Then it all clicked and I watched this video again.
Love your work ❤, I myself hope to explain some stuff that I am excited of.
thxc
I really want to help him back like you did when I get the chance
i also want to help him like you, when i am able.
500 russian rubbles
@@PauloConstantino167 Nope, its Indian Rupees
You sir truly deserve an honorary doctorate - just for this video. Your impact to generations of confused engineering and math students will forever ripple through our society.
I totally agree, as a very young engineer math and physics had been thought in only repetition but not in the actual application and manipulation we can do with them. How we can play and control math is a topic i find really interesting and in which im very new at it.
@@aaronlatapi2272 I taught the Fourier transform 'wrong' for ten years.... until I saw his method. his ability to explain things is ungodly.
and physicists
@@nosferato445 yes, he has both high IQ, really high empathy and the will to be listening towards others. Fantastic combination 😎
Fully agree
A extremely gifted teacher
It's crazy how Fourier was able to do this with just a piece of paper and his imagination, while I'm already struggling to follow this masterpiece of a visual explanation
And super computers at your disposal. Most people have little comprehension and appreciation for how important and inspired the giants whose shoulders we all stand upon are. The dedication and sacrifice our ancestors dedicated their entire lives to, is without parallel. The one thing they all had in common is a desire for fundamental truths. They were outcasts whose very existence challenged the staus quo. Just because we avoid conflict just to keep things copesthetic doesn't mean it is the proper path forward.
halihammer
Yeah, for some people... "built different" is an _understatement..._
The guys bibliography is also insane. Born an orphan, became a mathematician, later traveled with napoleon and become a member of parliament. All while creating the groundwork for a lot of quantum physics. Guy lived one hell of a life.
@@wfps488 WHAT? damn, I feel bad about hating the guy when our professor was not even trying to explain the beauty behind fs and ft, I didn't understand them for shit back then, I wanna blame the prof but idk.
@@wfps488 dude was an actual main character
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.
Just wanna echo that spirit. Has been a tremendous help to me to, even though my subject area is economics not pure maths.
Fourth year Physics/Mathematics student here and I've got to say first few times I did fourier transforms it was a nightmare and I really didn't know why I was doing it. But after just a few times I came to realise that they are much easier than people make out and so infinitely useful. So I wouldn't be put off of anything if it mentions that it has fourier transforms in it.
Yo dude, I'm in my 4th year at Manchester, hit me up with all the questions you want about undergrad physics. I can certainly remember how intimidating the whole thing is, so I would be honoured to do anything I can to help you along the path (I've just taken exams in GR, QFT [which is *all* Fourier Transforms basically] and Statistical Mechanics [also contains a massive amount of FTs], so hopefully I've picked up a few things you can make use of)
Came here to say the same: I studied in France and I too hated Fourier transforms... until I watched this video; I had no idea it was this elegant! Many thanks Mister 3B1B 🙂
I would say if you are confident on pure algebra and calculus, don’t worry about it. If you struggle with the concepts of what spaces you are transforming into, just don’t worry about it. That will come with time and experience. Just crack on with the maths. Worked for me, and I’m doing my PhD in spectral decomposition electromagnetism!
This channel is literally one of the best things that has happened for the mathematics community. Such valuable content.
@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
True, so true, my conceptual understanding of fourier transform has grown exponentially
I would go as far to say for me, it is the best channel on yt
I would also recommend mathologer
If this lecture was delivered in a class you would surely get a standing ovation.
I'm showing it in my class next week.
@@CaseyAtchison Well? What was their reaction?
@@akashchoudhary8162 More than one told me it's the most real science they've ever seen at their school.
@@CaseyAtchison So no standing ovation?
@@MrAlRats funny haha
Nobody is ever gonna read this, but i'm literaly mesmerized by the quality and accuracy of teaching this video posseses. It's nuts how well u explain such complicated things
I read that.
@@PhilippeSaner i appreciate bro
didn't read - just clicked thumbs up
@@simonhinterseer9974 well done soldier
Nope, we read it and we agree with you. I have 2 decades of constantly dealing with Fourier, Laplace, Smith chart, I came here for new perspectives. We live a revolution of teaching. Oh boy, I would have love to see this 20y ago.
I think you might be the best communicator on RUclips. 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!
Agree. Agree. Agree.
totally agree!!
Yeah! Agree..
This should be a template for all comments on RUclips. It's perfect.
Now now, let's not exaggerate.
I want to say one thing: Your skill in not only understanding and vocally explaining these concepts is so perfectly complemented by the animations you create that it blows all other resources on this topic out of the water. Even my college professors recommend this video specifically because, and I quote, "I could never create something so masterful that so aptly explains what is going on inside my head." Your skills are a gift to us all! I hope you always find as much passion in creating these videos as I do watching them.
It's incredible honestly, 3blue1brown and Sal Khan have made such massive impact; I might need to learn some chaos theory just to try to measure how we have profited as a species from just those 2. I would like to recognize educators in general for their hard work and passion, although, I think we can assess that a few individuals can be attributed a great deal of impact, similarly to say physics. There is a subset of a subset of individuals we can point at who we say have made great contributions, although if you point at them they almost certainly just point somewhere else; a giant standing on giant shoulders perhaps.
He is doing history
Become a supporter of Grant. I did....after watching his videos for a few years. His math videos are worth a few bucks a month.
@@benjaminknudson5997 You should include "StatQuest" as well in your list sir
In 20 min you've explained what my Analysis IV teacher failed to do during a year. You're fantastic!
why is it that I spent tens of thousands of dollars on a engineering degree, and yet these videos do a much better job at teaching me what the math actually IS than any of my professors... Keep up the amazing work!
university degrees are basically a business
It's because even someone who has never taken pre-calc can see immediate applications to, say fluid dynamics, with inverse fourier transforms if fluid dynamics is something he/she is into.
Those are the people that are likely going to use them in research roles or graduate school. Whereas vast majority won't ever touch them in a typical engineering job. It's like throwing out bait to hook one or two students a year.
Yeah, my main problem with my degree so far is they teach the pure math... not what it's for. Showing me equations upon equations does nothing for me without a base explanation of the usage.
People say these videos don't touch on a proper university education, but without this video I had zero clue. Now I can actually understand the lectures and the math 😅
@@SakiDGit makes sense they try to make you understand the thing rather than each individual application. As an engineer, the ideal would be that you comprehend it enough to recognize the opportunity to apply it in whatever context it would be useful. However, for that you need a strong and intuitive(without gaps) comprehension of how the math ties to the real world and the comprehension of the Fourier transform nature on top of that. But that's very rare. In general, people really struggle with abstraction, and math's favorite toy is abstraction, to the point of abuse. I would say that abstraction is part of the core of math itself.
But teaching people math this way is really difficult. Just as it is to teach anything without a bunch of gaps; a bunch of missing links of how things lead to one another. And its also inconvenient, for the system to test that and to basically turn you a basically a master of 10 or 20 subjects or areas. Managing learning is the toughest part of learning anything. The educative systems assures you a lower boundary for how bad is good enough. You get a better chance to get a much richer, faster and leaner learning by managing it yourself, but you also get the chance to screw it up badly; super slow progress or the absence of progress all together, much more and deeper misunderstandings, more gaps in your knowledge, etc.
I don't have an engineer degree. Nor have I took classes for that, but I consider myself an engineer; for me being an engineer is to understand the nature of things and influence them towards getting what you want or the closest to that.
After 13 years completing engineering , i understood use of Fourier Transforms. thank you sir.
Correct
bas formulae ratt ke aoge toh yahi hoga
@@AdityaX2703 What are you doing here? You better stick to Bhuvan Bam! Looks like typo in searching. Do you speak to your mom in that mouth? Yakk!
@@BharCode09 and i hate bb and indian youtubers
Thanks for saying that. Now I don't feel that much as such an idiot.
Cheers.
The amount of clever someone has to be to discover this stuff is insane
It's not just one person, it's hundreds of amazing people.
It’s not so much as to “discover” this stuff, but rather, using models and constructs to simplify the world around them in order to understand what was previously too hard to. These mathematicians were just so eager to see nature unravel in ways that unraveled cool secrets, that everything from calculus to Fourier transforms, etc. were built, rather, out of this curiosity.
The amount of clever someone has to have in order to explain it in such a simple way! At university my (very good and passionate Professor) took more than 1,5 hours!
I am a newb in the regard of creating math, but I would assume it has more to do with seeing enough relevant constructs and making a small or big leap based on alot of background. By no means do you need to be excessively clever to come up with this stuff, not even have a killer amazing amount of background. I just have come to believe that that's the case.
I know rite? Especially in math, physics and chemistry, sometimes I'm just sitting there wondering how on earth people managed to find this or that formula, or realize that there was this connection to that, which makes solving whatever problem 100 times easier. Something I still really don't understand is how astronomers figured out the orbital period, velocity and distance to earth of the different planets just by looking with their _eyes_. I also wonder how on earth Newton actually tested his equations of gravity to find out they were correct.
Your videos sir, are a gift to humanity
so true, I'm so glad this guy exist
berbudy exists*
So Trueee...!!!
I'm speechless with this work of art. The explanation of the underlying principles is amazingly clever, and the visual production is outstanding. I can't imagine the amount of hours needed to make all of this. It's an honor to have watched your video!
I study Applied Mathematics and I think of myself as of someone knowing quite a bit of mathematics and also (from what others say) having some sort of skills in transferring this knowledge in a pretty understandable way to other people. But compared to you... Well - YOU ARE SIMPLY A DIDACTIC GENIUS! The whole 'scenario' of each episode, the way you move from the things which are very easy towards the more difficult ones, the examples that you pick, the interpretations that you find, the visualizations... Each video is just a mathematical masterpiece! Thank God there was a moment in your life when you thought that your mission is to show the people the beauty of maths on RUclips. I cannot think of anyone doing it as good, as you do. :)
I am an electrical engineer and I studied Fourier Transforms in university and remember not understanding how it works. In my job I actually use Fourier Transforms to view the frequency domain, but again tools calculate it for me. When I viewed this video, it was the FIRST time in my life I finally understood how Fourier Transforms work! I absolutely love this video! Awesome job!
I'm a retired neuroscientist and now a part-time middle school teacher. I teach digital music production, and I rely heavily on Audacity software in my class. The noise reduction algorithm relies on Fourier transforms (which I have never understood adequately), and this video has helped tremendously! Thank you so much! What an intelligent way to reduce unwanted noise! Far better than a simple noise gate. Nice to finally understand the way it works. Sorta...
Don't you use fourier transform in interpreting EEG in neuro science?
@@ahreurink In my research, I never used EEG readings. I know they do use a complex noise reduction algorithm, and I'll bet it is the fourier transform. My work involved more of the molecular biology and behavior, and my labs mostly used animal models. Getting an EEG reading on a poor little mouse is not easy.
Until you end up with the NR gurgles lol
@@ahreurink Wow, neuroscientist to digital music middle school teacher is not a career path I would’ve guessed! Your interests and skills must be very diverse.
They teach digital media production in middle school? That seems so niche lol
I've been an engineer for over ten years (my roommate was the signals junkie and I was the embedded systems dude) and you are the first person to actually make me understand the derivation behind this thing.
> signals junkie
I'm stealing this phrase
This video is incredible, thank you!
Thanks Dan!
The Coding Train good to see you here!
You're my hero!
It's Dan!
You are a good guy
This is one of the highest quality content on RUclips.
15 years ago I was a chemistry student and I had to take exams on linear algebra and calculus. And I specialized in spectroscopy. That was a long time ago, now I'm in another sphere - computers, and I've forgotten a lot of details, though not the basic concepts. Let's just say, your videos made me connect a lot of dots in my mind. Incredible work, man. See, it did happen for me to teach - there was a schoolgirl next door, whom I sometimes helped with the lessons. Once she told me that she gets higher grades if I explain the lesson to her and that I was born for a teacher. Yet it's guys like you, that I take my lessons from.
As a math student I cannot believe there is a person can make math concept like this intuitive, amazing !
When you understand the main idea of Fourier Transformation finally in a youtube video instead of in a whole semester in university.
It's even better sometimes on RUclips
I can relate to that feeling too, but to be fair, it probably finally sunk in because you had built notions and worked with them before despite not understanding them to this level of intuition
this video should be proposed in EVERY FUCKING CLASS
@@orti1283 good point
I actually watched this before studying this in uni. For new people, this will shave off about 80 hours haha
Thanks, love your art, teaching style, analogies, and smooth delivery. Keep up the great work!
Rich boi
I often wish youtube had a better way of indicating HOW MUCH I like a video. This one would have scored high.
yeah, by youtube standards i liked this video and the one with the rat taking a shower equally
right! If I click like really hard, it just likes.
About 8 years ago, YT had a 5 star ranking system. I preferred it a whole lot more.. However, that meant you couldn't save the video in a "liked" list unless you favourited it.
Mikky They got rid of the five star rating system because the vast majority of ratings were either one star or five stars. People are hesitant to give a "bad" (read: less than five stars) rating to anything that has no significant flaws, even it is fluff rather than solid content.
Remember when youtube had star rating for videos? I always like that system better.
After 20 years of graduation, I now realize what I was learning back then. Thank you for your production.
same here
Every lecturer in my life has failed to learn me what Fourier transforms is but you did it in just 20minutes. Amazing!
Thank you for this! I have a BS in engineering, an MS in Computer engineering and none of the math, or signal processing classes I've taken explained this in several semesters as clearly as you did a few minutes. It all makes sense now. I finally get it. Bravo! Standing Ovation!
It's hard to overstate how valuable your videos are. They breathe life to difficult concepts which are often just presented without any motivation/explanation and expected to be taken for granted.
Words cannot convey my gratitude to you with making these videos, you are helping so many people all around the world to see the beauty of math, for what it really is. Thank you. You taught me more than any of my Math teacher ever did.
This is not only helping many people to see the beauty of math. People who understand these concepts more intuitively become better engineers, physicists, software developers, ...
Better teaching creates a better world. I wish there was a 3Blue1Brown for every field
@@p337maB Let's contribute to the society in ways we are capable, and eventually more 3B1B will appear. :)
@@mahxylim7983 That is true
1:50 Seeing a mathematical representation of a Dminor7 chord is all my jazz-mathematician soul ever needed.
♪ D minor 7 with 3 Blue 1 Brown ♪ - D F A C Intensifies
I just came back to this video again after a year or so just to re-watch it because thanks algorithm, and I came down into the comments to make this exact same comment only to find this one. :D
I take it you enjoy the Black Saint and the Sinner Lady then?
@@SoftwareEngineer-A I'm not terribly well-versed in specific jazz artists/bands, unfortunately. I've just had a few years' worth of band experience in high school and subsequent music theory osmosis vis a vis Adam Neely more recently. ^^;
@@calyodelphi124 Coolio. Well, if I have but 1 album to recommend, it would be The Black Saint and the Sinner Lady as it 1. fits the description, and 2. across the 2000 albums of which I have listened to and logged, it stands as the most perfect representation of music that I have personally ever had the pleasure of listening to. :>
I've had 5 years of undergraduate/graduate maths education and this is the best introduction to Fourier Transforms I've ever seen. Amazing. I must've done a billion Fourier Transforms and I've never seen it explained in this way. Plus the fact that you were able to derive the integral definition in a way that I feel anyone willing to learn it will understand easily is incredible!!! Keep it up man 👌
I somehow managed to get a computer science degree without once learning about Fourier transforms (though I narrowly avoided them several times). I'm not sure how I did that. But watching this video, they make complete sense! So often, "complicated" math concepts are taught purely symbolically, but understanding *why* they work, from the ground up, is extremely important -- and, for me, it's the thing that makes math fun!
I guarantee I won't remember the details of this in a few months unless I watch multiple times, but if I ever run into a need for Fourier transforms, I also guarantee I'll be thinking of this video to figure out what I need to do :) So thank you :)
IceMetalPunk Explain it to yourself a few times after watching the video a few times, then explain it to others so they also see the big picture. That is one of the best ways to learn it. 👍😊
This is by far the best, simplest, clearest and nicest explanation on the subject. Thank you so much! You're a hero
This is the best intuitive description of the fourier transformation i've ever seen. I've used fourier transformation several times, but it always seemed like magic. This goes a long way to make me understand why it works. These visual ideas are so important - and they are much easier to understand in a video than by reading a description of them in text. Amazing video!
From Neural Networks to Fourier Transform to Linear Algebra and Calculus... A Like is not enough really for all the work you are doing
sponsor them on patreon, it'd really help them, and us, in making more of these beautiful videos, more often.
SOOO TRUE!!!!!!!!!!!!!!!!!!!
I confirm that :)
Every time you upload a video I think: "eh, I've studied that before and these are supposed to work as an introduction for an unfamiliar audience, I'll listen to it in the background or something". And then every time it's a mind blowing approach. When you say something like 14:43 and I realise where you're going with it I'm always surprised and amazed at how elegant and cool you've made the topic.
That's why mental laziness and complacency is always a potential threat to any of us, even more so when you think "oh, I've already learned that" in your head, or you go "oh, I can't ever be mentally lazy; I have a college education and studied hard." I've been guilty of the same in the past sometimes but I keep these ideas in mind and actively try to be better. Remember: you ALWAYS have something more to learn. NEVER stop trying to learn more every day (or at least improve/further clarify your current understanding on subjects at the very least.) Having worked or studied hard in the past is no reason to get complacent in the *present* and think you're "done" already (that's just "self-justified" laziness, in my view.) That's the attitude I try to take at least ;)
Thanks for the input, Deathbrewer
Thanks! This video helped me a lot😄
Dang - I stopped taking math in 10th grade after my AP Math teacher took me out of the program because I didn't like doing all the extra homework. After going to school for music but becoming a programmer, I continued to learn more advanced math as needed. I've had random times where I've used the Fourier transform, but never really understood it or why it worked. This made it crystal clear and it feels good to fully understand what is going on both conceptually and in the notation. Thanks a ton for your time putting this together.
This is priceless!!! This simply can’t be found in any book! Thank you for the time put in for sharing these beautiful ideas!! :)) Best regards!!
Branislav J precious*
I'm studying engineering and I've been passing exams like calculus and acoustics where the concept of Fourier Transform (and Laplace too) should be well understood. But nobody ever explained it clearly or tried to, they just gave us the formula for the series and that's it, we basically had to accept it blindly. Researching on my own just gave me back analytical processes to get to the final integral, but without explaining the meaning of each step and just putting even more confusion in my head. I also like to make music so I've been playing around with equalizers and the like for a long time and I ended making up my own idea of how the frequency analysis actually works. But now in just 20 minutes you managed to fill one of the biggest gaps in my knowledge and I'm so happy you made this video, like from 14:29 on I really started seeing rainbows all around lol. Thanks a lot for this vid, I can't wait for the next ones
Same experience as yours. I had to accept the transform without understanding what was the thinking process of M. Fourrier. Pretty sure he was teaching it that way, when alive.
Upper grades in mathematics would be much more interresting with explanations like these. Professors are lost in the abstractions and have lost (or never had?) the art of transmitting the knowledge.
wwwKx same here buddy
Truth
Truth has been spoken here! This video is helping me to understand Computational Photography concepts (Processing,etc...)!
jshowa o maybe it's important to read a little bit of Shakespeare here and understand we are humans
After going through that, i believe it's important to understand stuff for the future of humanity, don't you find it odd that math is taught so badly? And that people that studied math a couple hundred years ago not more were chased and burnt to death? Something's going on here. But even more practically: don't you think that when you understand stuff you just are faster and better doing everything?
I remember struggling through the maths of Fourier transforms at university, many decades ago and I've long since forgotten it all, but this video is a very intuitive explanation. I just wish we had had such graphical illustrations when I was trying to understand it.
THIS IS SO BEAUTIFUL
I've been subscribed to you for a while now and have thoughts since the beginning that you have a very rare talent for explaining mathematical concepts but this video might well be the most awesome explanation of a mathematical concept I've ever seen. I've recently left academia after a PhD in Particle Physics so now I don't get nearly as many opportunities as I used to to get excited about Maths and Physics but every time I see that you've published a new video I get excited :-)
And of course as many others here, I really hope that people will start using material like this in lecture theaters. It gives so much more of a sense of the beauty of mathematics than writing on a blackboard ever could...
Sometimes - just *sometimes* - one needs access to a "double like" button.
Well done, 3B1B.
I agree my friend !!!!
In this special “sometimes case” I would be tempted to hit that double button multiple times.
I wish grant had a video on tensors, been browsing the internet and I can't get an intuitive feel on tensors.
Yep, one per turn :-)
actually on windows you can do it by pressing alt+f4
I've been using FT's most of my working career (40+ years) and this is the most insightful and fascinating explanation of the FT that I've encountered. How I wish this stuff had been available in 1980!! Brilliant.
This video gives me chills . How could a person come up with such elegant explanations 🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥🔥
I love how you went through building up the expression that would later be the "fourier transform" function. It's been my thing to make sense of equations. They're not just variables that you can plug and chug. Each term in a formula stands for something that should exist in the real world, and knowing what it means just fills my heart. Keep on fighting the good fight, Grant
You should get Nobel prize for your teaching skills. Mind-blowing...
I DID NOT expect to get pretty close to understanding Euler's formula in this video. When I first saw that, I thought it was going to take me forever to understand it, but it just happened passively while trying to learn something else... This is an awesome video
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!!!!
7:07 I just realized the reason it's giving a big spike at the zero frequency. When you move the frequency graph up, you're basically adding in another wave with a frequency of 0. The fourier transform still works
You're right!!
Woah, great insight
Yep, good point, it's the "DC coefficient", as we would call it in the context of the Discrete Cosine Transform (similar in concept to the Fourier transform) that is at the heart of MPEG video compression (though I'm sure that term is used in other contexts as well). As opposed to the "AC coefficients". Borrowing terms from electronics.
Look into the Dirac delta function. It turns out that the fourier transform of a constant is the aforementioned function. Your realization is more profound than you realize!
@@victorwilburn8588 correct you want a pure DC waveform molecular Attenuation Field Density , AC hum " 60 Hz "
Thus why in order to activate TRUE NMRFA of molecules you have to use Pure source of DC energy Alternating Current " Hum "contaminates a pure Sine wave frequency.. US War department R&D 1946 Infrasonic Waveform Weapons technology.
Honestly as a maths student in my 3rd of 4th year, watching your videos reignites my passion for it. Thank you, you're doing a genuine service to us all :)
It is unbelievable that there is such a simple explanation for the "thing" that the teacher has been teaching for months but left undefined! Congrats sir!
Your channel is LITERALLY more educative than all the universities in my country. Amazing. Your videos have seriously sparked my interest in mathematics.
Neil Deshpande , yah bhai tune dil chune wala baat kaha
And what country is that then
Rabbit Piet India :)
True that! I learnt more about Fourier transform in the first 10 minutes than I did in my entire second semester.
The feeling when everything clicks in is amazing.
Words can't even describe how incredible this video is. It literally made made me tear up of joy. You are the best teacher ever, period.
I am moved too, I just cant believe I finally got intuition for something I'm striving to understand for years in just 20minutes.
This isn't the way I pictured someone crying because of math
The work done in these videos is really some of the most encouraging, and pragmatic use of the Internet.
I have a PhD in Engineering and I never had a teacher explaining Fourier transform so intuitively. We have been defrauded by the academic institutions. Also, I have not seen a textbook explain this concept so elegantly like you did. I want my money back!
I'm an astrophysics postdoc, so I've done my fair share of FTs over the years, but this is easily the best explanation of them I've ever seen! I finally understand why they look like that
This is precisely what i want everything to be taught, with visualization and intuition that touches the heart of the matter. I admire you greately, man. Gotta start learning that insane animating skill !!
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. :)
The best, simple, easiest, and valuable video I've ever seen on Fourier Transform! Of course I had learned it from the class ,as a university student, but the professor taught us literally based on 'the formulas', didn't have any idea of give them 'a life'. This channel did it and now I want to say thank you over a hundred times to those who contributed to this video!
Life seems so simple and beautiful when I watch your videos. Thanks..
Wow can't wait for the uncertainty principal!!
I have to say you give me so much motivation for my studies (physics). I think without you my grades would be so much worse than they are now!
I'm just a musician wanting to understand more about sound...haven't done math since high school...this video was probably the first time I have enjoyed math...ever. Amazing stuff!
This is probably one of the best videos in RUclips history
engineer here... this is one of the greatest videos ever made... awesome job
This might be the best math video on RUclips.
I have a master degree in Mechatronics. I had lectures in Signal and picture processing. I learned how the transformation behaves, its properties and what happens if you change the function, shift, strech it etc. But nobody gave us an analogy to understand the tranformation formular itself. Thx man. Now I have a new perspective to this topic.
Engineer getting back into math. Your videos are awesome
I took a class on this in College and I still had no idea what Fourier Transforms were when I finished. The first 2 minutes and 22 seconds of this video made it abundantly clear. Well done! Clear, visual, best-in-class video explanations like this, that can be watched over and over again from the comfort of your home is a game changer and will disrupt the traditional and expensive College education system as we know it. I think Khan Academy is on the right track. If they start giving out degrees it's Game Over.
The vision of the future
That's so true mate !
i think you are somewhat hiased. these types of explanation is mostly apreciated by people.who already got ass burnt by college courses and were forced to solve problems/projects/whatever your uni is up to, then forced to somehow "make the notions work for them". at THAT point those 3 minitues made your brain snap and say "that's it!" and probably lots of electronics, signal, automation notions came together (look at how similar are those patterns to equilobrium criteria in auyomation control).
are we sure it will work the same the other way around? without that ass burning college part?
me too bro. understanding concept to the core is what i also seek, but tradional college is just a degree machine, where u gobble all formulas and vomit in paper. no idea what u studied in ur entire degree. i also love khan academy. :). do u know another channel or videos which can help great in college level math. like partial derivative,
@stephen von crven Exactly!
Give this guy a Fields Medal for discovering the best way of teaching Mathematics.
I am literally speechless, I don't know how could I thank you for this stuff.
I wish our teachers would have taught us in that fun way, where maths feels natural.
Did you really understand all that ?
@@n.p.9997 Yeah, bcoz of mathematical background.
If I had had a chance to look at your vdo 30 years back during my electrical engineering classes, I would have fully grasped what I actually completely lost back then. My goodness, your explanation and graphich presentations are unmatched by anyone on this planet.
This guy is a genius at explaining concepts. Only person I follow enough to support on Patreon
"chaos and chaos and chaos chaos chaos, and whup things line up pretty nicely" *repeat*
-- My life
I read this comment exactly at the same time he said it in the video lol
love the WHUP
If you think about it, events in life are kind of like different frequencies that sum up
Good one!!
The amount of work put into this is astonishing
This might be one of the best videos on RUclips ever :)
Funny how we pay loads of money to learn this stuff at university, yet we all still come running to free online video lectures because no professor can match them in terms of quality.
I was just thinking about how the reason I dislike this kind of RUclips channel is for the same reason I dislike other similar channels, such as Veritasium, Numberphile, SmarterEveryDay and VSauce. The trouble is, you aren't really learning anything.
In University it usually takes a long time and you have to start from the foundations and work your way up through the rungs one by one until you arrive at the point where you can follow what you've learned into the workplace and do it professionally.
This kind of channel uses the "wizzbang" or "wow" approach of endlessly cherry picking isolated curios and well known and popular but poorly understood ideas.
In University after this you would be tested by having to produce maths or write programs which use what you've learned to show you can. You don't get that here and it's my guess almost nobody who watches this video goes on to actually sit down and write their own FFT. In the end, you just add it to your store of useless information.
@@vapourmile Actually, I got to disagree with you on that one. I think you misunderstand the goal these types of channels have in mind. They aren’t academically ‘rigorous’, because such long-winded video’s would only be watched by those already schooled in physics/mathematics. The aim is to help conceptualize idea’s and inspire people to investigate for themselves. The importance of communicating science to the general public is something that’s often overlooked.
As for 3B1B, I actually did learn something from this video. My university did nothing to provide me with a good concept behind Fourier transforms. Basically, I was handed a 10 page document with all sorts of mathematical wizardry going on, so that by next lecture they could use Fourier theory. I might have kinda understood the derivations, but I missed any visual intuition as to why Fourier transforms worked. After watching this video I went back to that document and it made a lot more sense.
I believe many people just end up memorising the formula’s, without much understanding. It’s a lot harder to find new applications for a theory if you don’t really understand where it comes from and what makes it work.
@@vapourmile I mostly agree with you here. The aim of the videos isn't to give a deep understanding, but to give the viewer a neat intuative sense of what's involved in the topic.
However, I love these channels! It makes these difficult topics accessible for, well, anyone.
And in my case, I often come to these sorts of channels to supplement my academic learning. I find lectures to be quite dry and difficult, but when I combine that rigorous understanding with this intuative understanding, that's when I'm most easily able to work with and exercise these ideas!
@@petermarsh4578 Exactly, people often think that this is all formal academic course teaches you and say "school and college bad!!!". Videos like these are meant to explain the bigger picture of a subject, not to replace rigorous academic study of it. At best, these are meant so that the general public understands more (not all) of the topic, and as a "companion" for those studying it in an academic institution.
i had some excellent professors, however it doesn't really matter too much if the professor is bad or not since learning math takes a ton of self study anyway. The people complaing about bad proffesors may have valid criticisms, but when you do research you're basically on your own and it doesn't really have much of an effect on your education, though all your colleagues will be massive math nerds.
I can watch it a hundred times and still not get tired of it. I can only imagine how difficult this would have been for me without this kind of explanation
Because he is overly complicating the concept
I can watch it a hundred times and still not get it. :/ I just do not get this rotating spirograph thing at all.
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.
hard work is food for the soul
All right Abdul, closed book exam in an hours time - hurry up.
@@sharat77 LoL
Thanks!
That has to be the best explanation of the Fourier Transform I've ever seen.
Perfect 5th, then minor 7th chord. a great start to a great video.
it's insane to me that your ear and brain can do what a mathematician does on paper instinctively with a little practice, yet the same is true on paper still; furthermore, the math can take these concepts and turn them on their head and back again.
By the end of this video, as expected (at this point in my experience with 3b1b), I am intrigued, astounded, and curious. I have felt tempted to give up on my passion in math recently, as I've taken up a strong interest in music, but I've been proven time and time again that the two work together, almost interchangeably.
Thank you for taking the time to make these videos. Your talent in visually explaining intense mathematical concepts persists like none other.
When is there going to be a series similar to your Calculus and Linear Algebra Series, but for Diff Eq and MultiVariable??
with love,
a subscriber.
I have finished my Electro-technical university 22 years ago.... FT was one very important thing ... and only after 22 years , I really understood it ... THANK YOU FOR THIS VIDEO
I almost cried watching this video. Such great explanation! Everyone deserves this
it is a thing of beauty
bloody hell me too ahahha
Oh.. My.. God
This thing just taught me more math that 2 yrs of Engineering lectures couldn't teach me
taught you MORE than 2yrs of lectures COULDN'T teach you??? what 2 yrs of lectures COULDN'T teach you is almost infinite, so your statement becomes trivial. apparently X yrs of language and composition lectures likewise failed to teach you how to express yourself accurately and precisely. maybe you're just not college material. or maybe you need to learn to think FIRST and only speak afterward, rather than blurting out the first thing that pops into your head.
Dude... perhaps English isn't his first language. There's no need to insult or put someone down online due to a simple grammatical error.
+Adam Nasir - if you think my comment to pranit was insulting or contained a put down, then YOU are an touchy-feely politically-correct IDIOT. see the difference? THAT is an insult (even tho conditionally true). i corrected a blatant LOGICAL error that had NOTHING to do with the commenter's native language, and everything to do with careless sloppy composition. sloppy speaking (or writing) is the surest barometer of sloppy thinking. also, don't you think pranit can defend himself if he felt the need? aren't YOU the one being condescending by ASSUMING that pranit needs you to butt in and defend his honor? how arrogant and presumptuous, not to mention passively-aggressively insulting to pranit. or are you too "logically challenged" to follow the implications of your post to their inescapable conclusions? dimwit.
+John Michael
gr8 b8 m8
John Michael You two are having a misunderstanding because judging from the type of answer you both decided to give...
a) you made logical approach, focusing on the logic problem of the original post, whereas
b) Adam Nasir interpreted pranit pawar's message a different way by guessing its intended meaning and perceived your message probably as quite blunt.
Therefore - and this is my perspective and how I interpret the collision of you two - you two may be talking about the same topic but on two different levels.
Whether or not this conversation makes sense is a whole different question, because we don't know how pranit actually meant his message to be understood. Was he being sarcastic? Was he having a bad day and he used this message to express his emotional situation? ...which btw isn't more than a tiny snapshot of what pranit really thought when he wrote this. Or are we thinking waaaaay too much about all this, because pranit just wanted to express that this video is genius because it explains a complex topic in so little time?
If the topic is important to you it can help to ask the one who gave a statement, how he/she means it. That helps you understanding whether your thoughts are relevant. Or don't ask, speak your mind and prepare for conflict. ;-)
Communication is a beast. 🤙🏼^^
Such videos should be on the beginning of every university class. Purely explained on animation. Finally i understand how it works after 10year of my university graduation.
I have no words to say how much impressed I am by this video. More than twenty years ago, at University, I was literally going crazy just trying to understand where those formulas were coming from and what they were trying to represent. I no longer have to know that, but still it was in my mind. So today, pushed by laziness and curiosity I've gone through this video, which relly blew my mind. Really a great job!
Brother, You deserve an applause, because of the Explanation and the Modeling of the video. I really appreciate your work, and all of us are thankfull to you, God bless you
I have Master degree of mechanical engineering and your videos helps me a lot truly understand math and physics. Thank you so much. Your brain is beautiful.
Now I see that complex numbers nad FT it is just smart mathematical tool.
Oh my lord I though that was gonna be so complicated but it’s so simple! You are a god level teacher.
This channel is amazing.I wish I had this channel during my engineering days.
Absolutely, positively, the most stellar and intuitive introduction to Fourier transforms I have ever seen.
You have far better explained, in just 20 minutes, what my uni lecturer ever could in a semester back in the day.
My favorite videos on this channel are the ones where I think I have a pretty good intuition on the topic already, but I still leave the video feeling like I learned something new.
Fourier Transforms are ubiquitous in EE and I wish this resource existed when I took my first Signals and Systems course in undergrad.
As an electrical engineering graduate I SERIOUSLY wish this had come out while I was still in college, SUPER insightful and it all comes together and makes SO much more sense now. I always thought of it as a shorthand "switch" back and forth between frequency and time domain, but the polar graph and Euler's equation makes SO much more sense.
Josh Garber well, technically it IS a shorthand switch between freq & time domains, bc interpretation & manipulation are easier in one or the other domain, depending on the circumstances. But you're right; the explanation in this video is superb & goes beyond just freq & time domain.
If I ever become a professor, when the moment comes to teach Fourier Transform, I'll just put on this video and sit with the students. There is absolutely NO better way to explain this concept
Our laser physics prof actually linked this video for us to watch as an introduction to fourier transform!
@@StrawberryLegacy I like it when profs are looking a bit behind the edge and are actually giving you other good sources to learn other than their own script
This video helped me tremendously. I have only one complaint about this video: I had trouble figuring out exactly where the 'center of mass' was supposed to be because I wasn't sure if the mass-density of the wire wrapped around the circle was uniform, or whether it was the mass-density of the wire in Cartesian coordinates that was uniform, or both by somehow scaling the circle or wire to make it so. Only by the end of the video was it possible for me to deduce that its neither, and the mass-density is instead equal to the radius times the 'dt' infinitesimal of the unit-circle arc length. It took me 40 minutes instead of 20 minutes because I had to sort though my confusion first. But I don't care. I am extremely grateful for this video. It was awesome. I'm a physics-major and I never understood the Fourier transform until now because my university didn't go over it carefully enough and their continual torrent of homework assignments never allowed me to look into it independently, and yet, they required me to use the Fourier Transform after only giving me a highschool-level explanation of what it did, and this triggered my ADHD terribly because I need to know everything. I am extremely grateful to you Grant, and also a little annoyed at my University.
The world needs such videos to develop the right attitude and the mindset for the real learning. Amazing and hats off.
We learned things in our schools not only in pretty boring way but also in the useless way that prohibited us to appreciate the beauty of nature.