What is a Fourier Series? (Explained by drawing circles)

What is a Fourier Series? (Explained by drawing circles) - Smarter Every Day 205

Рет қаралды 3,618,659

Күн бұрын

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Doga's a super smart dude who writes a Turkish blog "Bi Lim Ne Güzel Lan" that roughly translates roughly to "Science is Awesome Dude". We had a lot of fun working on this together. He would really appreciate it if you checked out his blog. The fun thing is that most of his articles transcend language.
Doga’s Blog (written in Turkish):
bilimneguzellan.net/
Doga’s original Fourier Series blog article that blew my mind:
bilimneguzellan.net/fuyye-serisi/
Click here to tweet him "thanks" for / bilimneguzellan
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Destin

Пікірлер: 5 000

@benschofield1361 5 жыл бұрын

Holy cow, Destin how are you today?

@smartereveryday 5 жыл бұрын

Thank you for asking. I'm actually quite tired if I'm honest. I worked all night to get this video done. We also uploaded a new podcast episode last night so it was kind of a confluence of stuff stacking up, (not unlike the sine waves in this video). It's a cool podcast episode though. It's about a rather interesting time I tried to pee in a bottle and was literally stopped by physics. I think you'll like it. www.nodumbquestions.fm/listen/2018/12/9/049-peevnrt Thank you again for asking how I am. I'm a real person and a lot of time people treat me like a content generation algorithm. Super cool of you to talk to me.... the human. Thank you.

@benschofield1361 5 жыл бұрын

@@smartereveryday I can assure you it wasn't in vain, this was super interesting ! Thank you for making these awesome videos. I hope you get some well deserved sleep tonight!

@Discostew2 5 жыл бұрын

@@smartereveryday loved the podcast Destin, had me dying of laughter while you shared the pee story.

@Blox117 5 жыл бұрын

@@smartereveryday get back to work, bot! who told you that you could pause making videos?! lol

@Chrisamic 5 жыл бұрын

@@Discostew2 I haven't listened to the podcast yet, but I think I know where this is going LOL.

@lbmetei7596 4 жыл бұрын

Big fan of Mr. Fourier. He made my life very difficult.

@vishnubharathit6192 4 жыл бұрын

LOL

@samamani5423 4 жыл бұрын

:))))))))))

@halonothing1 4 жыл бұрын

Yes, but without him, you wouldn't be watching this.

@sanamazarniya8092 4 жыл бұрын

looooool

@riseabovehate9476 4 жыл бұрын

@@halonothing1 lol

@TheCodingTrain 5 жыл бұрын

Well, I guess I know what I'm going to try to program on this Friday's live stream!

@owendeheer5893 5 жыл бұрын

Well, I guess i know what I'm going to be watching on Friday!

@MisterDerban 5 жыл бұрын

please do !!

@noxabellus 5 жыл бұрын

I was just thinking of you! This is a perfect match for your show :D

@markoftheland3115 5 жыл бұрын

Destin: "How did you make it?" Me: "processing? p5js?" Doga: no Me: :(

@plor1261 5 жыл бұрын

I guess I know who I'm subbing to next!

@AsianBrozGaming 4 жыл бұрын

1:53 "sine ways are probably the simplest kind of waves right? the second most some kind of wave is..." me: cosine waves him: a square wave. me: oh

@darshandabrase3265 4 жыл бұрын

Hey, you stole my thought.

@no_t1es 4 жыл бұрын

_sad cosine noises_

@gamingbloopers6055 4 жыл бұрын

Rerin YL dude, stop ruining the fun with your facts

@XenoghostTV 4 жыл бұрын

@Rerin YL You don't say?

@jarvisluo5723 4 жыл бұрын

@@gamingbloopers6055 it's true tho. It's a flawed joke cuz it's not based on facts. That's not ingenious nor fun.

@akuljamwal3085 3 жыл бұрын

Dr. Doga hasn't looked happy since his pronunciation of GIF was corrected

@atlas_19 3 жыл бұрын

LMFAO

@yashrohatgi6053 Жыл бұрын

Ya see Norm, GIF stands for Giraffe Interchange Format, so it has to be pronounced that way...

@arnaudsimon3265 Жыл бұрын

Ahahaha so true

@cchollands Жыл бұрын

Even ChatGPT agrees that the hard G pronunciation is more common. Take that, Destin.

@smartereveryday 5 жыл бұрын

"It looks like a whip".... (Starts studying whips)

@charadremur333 4 жыл бұрын

@@DemirSezer not no more. But yeah.

@charadremur333 4 жыл бұрын

Hi dustin, have you herd about of powered paragliding? Its pretty cool, can you do a video about how the wing works? Thank you for your'e time.

@michaelrose93 4 жыл бұрын

Whips have all sorts of uses...

@Familia_nepal_nepal_do_mal12 5 жыл бұрын

In Physics we have a saying: If you have one problem needs to be solved with fourier series, then you have 2 problems.

@wsjacksonjr 5 жыл бұрын

Imagine how hard it would be then with a sevenier series!

@adamvav2730 5 жыл бұрын

Mr. Jackson I like you

@alexanderstohr4198 5 жыл бұрын

fourier => frequency analysis - just pick the standard modules from the shelves if you are having to do it...

@corgikun2579 5 жыл бұрын

@@wsjacksonjr your last name brings me nightmares (Classical Electrodynamics book by Jackson)

@nazishahmad1337 5 жыл бұрын

@@corgikun2579 but it's a really really good book if you're having concepts cleared from something much more basic like the Griffith's electrodynamics

@jerrygundecker743 4 жыл бұрын

I like the part where you asked him to explain it. You can see him stop, (momentary exasperation) and rethink it to put it into words. We actually saw his brain change gears. Loved it.

@naonao77090 2 жыл бұрын

Leaning about the harmonic series rn. learning that not only can you make just about any sound just by adding simple sign waves together but you can also draw by adding sign waves is absolutely blowing my mind.

@sunscream8502 5 жыл бұрын

KZfaq should recommend these types of videos to everyone.

@Aemilindore 5 жыл бұрын

it did!

@ov3rkill 5 жыл бұрын

Instead they push their algorithm towards flat earth. lmao.

@gabrieldoudna6570 5 жыл бұрын

ben shapiro wants to know your location

@mrzoldik201 5 жыл бұрын

@@ov3rkill it's fact , earth is flat

@neocortexlab 5 жыл бұрын

@@ov3rkill that`s becouse the earth is realy flat in the place where youtube office is

@EAHowe 5 жыл бұрын

I had Dr. Doga for my Physics I and II classes my freshman year. Crazy to see him on this channel.

@Johnquistador 5 жыл бұрын

Same here buddy

@egemenbags5465 4 жыл бұрын

Which college is it

@andrewkarsten5268 4 жыл бұрын

Egemen Bağış he said tech

@LetsbeHonest97 3 жыл бұрын

@@egemenbags5465 Georgia Tech

@zeynabrahmani2248 2 жыл бұрын

How can we keep in touch with Doga?

@TrevorHammonds 4 жыл бұрын

Your channel is truly one of KZfaq's gems. Keep up the terrific work!

@sef83 Жыл бұрын

Doga (Doğa, more correctly) means "nature" in Turkish. So "nature" tries to understand "nature" by using math :) proud of him!

@SpaceSnaxxx 5 жыл бұрын

4:23 "I made this amazing art tool and you're correcting my pronunciation?"

@we4selradio591 5 жыл бұрын

Graphics Image Format. why would it be Jif? we don't say jraphics.

@Trias805 5 жыл бұрын

@@we4selradio591 This

@commanderoof4578 5 жыл бұрын

Unless i am wrong he was joking when he said "do you know its pronounced jif" And if he wasn't joking then he is flat out wrong and it would be a correction at all

@Novumic 5 жыл бұрын

@@we4selradio591 jpeg, sonar, laser, scuba, pin, NASA and many more... google their meaning. If you want to use that "rule", then you are going to lose every one of those cooler sounding acronyms.

@Anon54387 5 жыл бұрын

I always pronounced it with a hard g. The difference being that no one said diddly because they knew what I meant and it was irrelevant to what we were working on. None of my classmates flunked out of engineering school due to different pronunciations.

@lauraleeane 5 жыл бұрын

As a grad student who uses Fourier transforms daily, it is incredibly valuable to watch well made videos like this that take a step back and see the beauty behind the math. Often in the classroom we focus to much on the answer and not enough on the beauty behind the math to get the answer.

@bennytyty 5 жыл бұрын

If you haven't seen it yet, 3blue1brown is an amazing channel that's full of visualizations that show off the beauty of math.

@ScormGaming 5 жыл бұрын

You need to watch 3Blue1Brown's visualization of the Fourier transform.

@cakcakstudio7551 2 жыл бұрын

I love it when you explain the science behind things. Those of us who watch the science, engineering communicator channels, do so to get a basic understanding of how. certain formulas or topics work. The way you explain things is so helpful.

@marcpaul8245 4 жыл бұрын

Finally, thanks to you, Destin, and Doga, I can visualize additive functions with a Fourier series! Thank you!

@jima1135 5 жыл бұрын

His reaction to your correction of how to pronounce "gif" was perfect lol

@SomeDumDum01 5 жыл бұрын

Jif

@abhinavgupta9990 5 жыл бұрын

It's not gif, it's gif.

@MouseGoat 5 жыл бұрын

@@SomeDumDum01 gif gif gif, to the day i die! the internet was build on gifs... not jifs :D

@XypherOrion 5 жыл бұрын

@@SomeDumDum01 Irrefutable proof that its a hard G, you have to spell it with a j to get the idea across. XD

@victorqwilleran3331 5 жыл бұрын

@@MouseGoat giraffe, ginger, German, gif.

@domainofscience 5 жыл бұрын

That is such and awesome visualisation of the Fourier series! It also makes me wonder what your logo sounds like. You could play each of these circle bundles as a musical note that is made of all of the sine waves, so your logo is a chord of 4 notes. I wonder if it would sound nice?

@TrentSheather 5 жыл бұрын

You're right! After all that I forgot it was a collection of sine waves and would totally have an associated sound. I hope Destin finds it, even if it is just 4 tones.

@massimookissed1023 5 жыл бұрын

Ima gonna hazard a guess that it sounds awful.

@Blox117 5 жыл бұрын

it would sound like noise

@Blox117 5 жыл бұрын

@@TrentSheather any type of wave can be considered "sound" not just a pure sine wave.

@MartinBuzon 5 жыл бұрын

Ok you are right and wrong. The thing you will hear is the TEXTURE of the sound, thats really interesting. But you can perfectly change the pitch to whatever you like by changing the speed of reproduction, since frecuency is how fast it plays. So it can sound really cool

@mm-qd1ho Жыл бұрын

One of the best parts about this is when Destin says that, just as a complex Fourier Series is the sum of all its simple shapes, a very complex engineering project can be the sum of relatively simple concepts and parts. Nice analogy!

@Rujenz7 4 жыл бұрын

Welcome to the comment section, where we have: 90% about the GIF pronunciation 10% regarding the Fourier series

@triplea7071 4 жыл бұрын

I know right

@adisuresh7263 4 жыл бұрын

In which category should we classify your comment lol

@mophab 2 жыл бұрын

Destin opened the can of worms by commenting about it. If he had let it pass, people wouldn't comment.

@joescott 5 жыл бұрын

He says "gif". I like him.

@NautilusGuitars 5 жыл бұрын

Fancy seeing you here!

@iankelk 5 жыл бұрын

Joe Scott and Destin corrected him to gif and I don’t know how to feel. Btw it’s pronounced “gif”

@garydunken7934 5 жыл бұрын

Very appropriate, because he is gif-ted.

@TheStaffmaster 5 жыл бұрын

@@NautilusGuitars THERE'S DOZENS OF US!!! :p

@lambdastudios4083 5 жыл бұрын

Its Gif, with a hard G. It Fundamentals book agrees with me

@jaidenboucher0 5 жыл бұрын

I have never left one of your videos without a smile on my face and this is no exception. Thank you so much for doing what you do.

@AlexanderBukh 5 жыл бұрын

so true

@sodiboo 2 жыл бұрын

This demonstration of circles and the wave is what made it click for me. I've seen Fourier transforms and explanations for them, seen how waves add and also seen it used to describe that circle thing that can draw any image. What i never saw until now is how these are related and how a speaker really works. like "it moves with the deep frequencies and then during that motion it also moves faster with the high tones" is what i've heard, and that's good and all. I never knew how a computer would actually compute such a wave, but it makes sense now! You stack the circles and track the Y value. There's probably some elegant way to do it easier in code, but it all makes sense now!

@AmericanPeasantry 4 жыл бұрын

This is true brilliance - to be able to take the most complex functions in the universe & simplify them to where a child can understand! Our family loves your work, Destin! Thank you for being such a great teacher!

@Freizeitflugsphaere 5 жыл бұрын

This is what kills me at university at the moment...

@TF23DayRespawn 5 жыл бұрын

I took PDEs about a year ago, ughhh that class was a pain, good luck!

@edeneden97 5 жыл бұрын

Watch 3b1b video on it

@willfrank961 5 жыл бұрын

Just echoing Eden's comment: 3blue1brown has an excellent video on the furier transform here on youtube.

@Freizeitflugsphaere 5 жыл бұрын

@@willfrank961 Thank's guys!😅

@Mickyleitor 5 жыл бұрын

Me too, Im doing it for the second time 😅

@chandrakiranyada2253 4 жыл бұрын

I've used fourier series in numerical methods but this video made my mind blow away...brilliant.

@kennethduncan4643 3 жыл бұрын

This is going out to my audio engineering buddies. It's super interesting to see a whole different visualization of waves we like to mess around with in synthesis.

@harrymoschops 5 жыл бұрын

Great video, did a bit of digging on the subject and I discovered reference to a famous paper by J.W. Cooley and J.W. Tukey from 1965. Their work utilised Fourier analysis and led to a radical increase in computing speed by exploiting the binary notation inherent to computers and the symmetry of sine waves. This leap in computing power is what enabled the effective storage and recall of analogue recorded sound via digital bits of information.

@JiveDadson 5 жыл бұрын

They re-discovered a way to quickly compute discrete Fourier transform solutions. (O[n log n]). Gauss had discovered the method in the early 1800's, even before Fourier published his work. Then people forgot.

@OF01975 5 жыл бұрын

Bullshit

@gumball1216 3 жыл бұрын

Doga's face when you said jif had me in tears

@ianchinsor9248 3 жыл бұрын

This is without doubt the best way to teach the Fourier series. I saw this and it clicked immediately after hours of confusion studying books

@XevianLight 5 жыл бұрын

That animation of making the SED logo with various instances of N should be your intro.

@alejo8alau 4 жыл бұрын

Cool idea

@ImXyper 3 жыл бұрын

6:40

@Jimanator 5 жыл бұрын

3blue1brown and Mathologer both have wonderful videos on this subject

@leitecunha 4 жыл бұрын

Wow, those thousands circles moving like crazy and drawing a perfect face was beautiful. I'd love to put them in 3D and see them layered in VR 😄

@jacksonmorris-thring644 3 жыл бұрын

Something that really made me appreciate the power of the Fourier Series was my 9 hour Fourier optics practical I did this year. Essentially, you collomate a laser beam and put it through a hexagonal matrix-hole’d piece of plastic. You’d pass this through a Fourier lens and it’d leave you with an effect that essentially allowed you to seperate higher order frequencies from lower order frequencies going from the centre outward. Through using another filter, you can then block those said frequencies, and make “false” images. You can change the shape of a sticker-star’s shadow cast onto a ccd camera. Blew.my.mind!

@apeters8 5 жыл бұрын

Just want to point out that he's not a student! He's Dr. Doha!

@GoogleModerator 5 жыл бұрын

We are all students of science. Okay, I had to :)

@chaka5199 4 жыл бұрын

Dr. Doha. Thank you.

@lukenelson556 4 жыл бұрын

Doga, with a G according to the video

@gokaytaspnar1355 4 жыл бұрын

its Doğa

@DrTWG 4 жыл бұрын

I'm no mathematician or coder (MD by trade) but managed to get a square wave going - much like the one above with all the circles whipping around - using Javascript & p5 library. It was actually easy . The series is basically sin(wt) + sin(3wt)/3 + sin(5wt)/5 ................ t is your time step , w = freq . The more terms the squarer. Getting the graphics looking good & moving was the tricky bit.

@thehotdogman9317 3 жыл бұрын

Ahh, interesting. My guess is if you used varrying lengths of the n coefficient in sin(nwt) / n, you could derive any organic shape in nature.

@CammaProjects 2 жыл бұрын

Also add the starting phase of each harmonic sin(wt+phi1) + sin(3wt+phi3)/3 + sin(5wt+phi5)/5 ecc

@lukasmodry196 Жыл бұрын

I love it, my teacher from algorithms first told me about this and i am absolutly amazed. Keep going!!!

@nicole-secondaryemail-mort9617 4 жыл бұрын

Love what I learned here. A glimpse into a whole world of math and waves and their potential. Not my academic discipline; which is why I really appreciate such a visual and intuitive walk-through. Thank you!

@Ozzah 5 жыл бұрын

I pronounce it "ga-jif" to make sure I cover all my bases.

@ZardoDhieldor 5 жыл бұрын

How to annoy every geek with only one word.

@winsauceiswin 5 жыл бұрын

Brilliant, I’m going to use this 😂😂😂

@IvarHuisman 5 жыл бұрын

Jyff is also a good one it approximates the spelling as a word G I F JYFF

@part-timepartytime9621 5 жыл бұрын

Zhaiff for life! Zhaiff for life! Zhaiff for life!

@KingBobXVI 5 жыл бұрын

"Gzheyf" - just to make sure it's wrong for everyone.

@FruitNBootNJordN 5 жыл бұрын

“This transcends language” 😭😭😭 👌🏼💯 this was that cool, love it!

@738polarbear 4 жыл бұрын

I love watching smart people explain stuff . the smarter they are the humbler they seem to me.

@thesaltedlamp3444 3 жыл бұрын

This was incredible! I can actually, finally, visualize the usefulness of, and the mathematics behind Fourier math!

@LivetoshootNC 5 жыл бұрын

Wow. I wish we had visualizations like this when I was in school. These videos must inspire young engineers and science students.

@quahntasy 5 жыл бұрын

This is such an intuitive way to understand Fourier series. Wish we were taught stuff in this way.

@lorenpearson1230 5 жыл бұрын

Some of us were. Not sure what has happened in the last 30 years, but maybe it is coming back through these visual tools. Imagine though that Fourier and his contemporaries had to 'see' this to make it work.

@realedna 5 жыл бұрын

It's just the visualized addition of some major complex fourier components in the complex plane animated with time. So it's just a random analysis result! If you understand complex numbers (incl Euler's formula), cross correlation and linear combination/algebra, then you can understand fourier series fully. Most of which wasn't explained in this video at all!!

@richardsteen4340 2 жыл бұрын

It is truly a great visualization to see how stacking/mixing sine waves actually produces different wave shapes.. Too cool..!! Love your Channel..!!

@paulswanson3132 4 жыл бұрын

You just BLEW my mind dude!! The simplest building blocks, like circles, can create ANYTHING!

@enumaelish11 5 жыл бұрын

What a beauty! This video just explained a thing I'd been trying to understand, so thanks! Now I' a bit smarter :D

@TitoTheThird 5 жыл бұрын

2:35 Those "wipers" are called "epicycles" in Ptolemaic astronomy.

@verwehtverweht9053 5 жыл бұрын

Exactly... I also remembered that medieval astronomers were forced to use epicycles in order to explain the periodicity of the planet's orbits as seen from the Earth, and assuming the Earth in the center of the universe...

@trevorjaster4072 5 жыл бұрын

How are they used in astronomy

@verwehtverweht9053 5 жыл бұрын

@@trevorjaster4072 They aren't. They were used, 500+ years ago, in order to explain the motion of the planets, as they assumed, at that time, that the Earth was at the center of the Universe.

@TitoTheThird 5 жыл бұрын

@trevor: Epicycles were used to explain retrograde (or backwards) motion of the other planets in the Earth-centered Ptolemaic astronomy.

@lbblackburn 5 жыл бұрын

And now the phrase "adding epicycles" generally means to make some theory work by adding absurd complexity.

@clancybenedict6647 4 жыл бұрын

First SmarterEveryDay video I've seen and even the promo was cool lol. This is amazing. Subscribed

@ponyote 2 жыл бұрын

The look you got for the correct pronunciation of gif (thank you!) that was blistering. You rock, Destin.

@Hexanitrobenzene 5 жыл бұрын

"...let's challenge him !" Destin shows a logo of SmarterEveryDay. I'm like, "Come on, man, you can't approximate that with Fourier series. That's a multi-valued function!" Doga constructs a graph with 4 parametric functions, each approximated with Fourier series. I'm like "Oh... o_0 I stand corrected." :D

@blancaroca8786 4 жыл бұрын

Here too. I am really annoyed with myself for not knowing about doing Fourier representation in 2d like that.

@nanamacapagal8342 4 жыл бұрын

Apparently you can make a courier series that approximates an image without doing the X and Y sines separately. Instead you use e^2iπt. As t progresses, e^2iπt goes around a circular path. You can then add several of these circular paths together. 3blue1brown has an excellent video regarding this topic.

@Hexanitrobenzene 4 жыл бұрын

@@nanamacapagal8342 Excuse me, but I think you missed the point. Series with e^2pi*it terms is just another representation of series with sin(2pi*t) and cos(2pi*t) terms. Both of these can only be used to represent single valued function of t. Say, you have a circle of radius 1 centered on an origin of cartesian coordinate system. It cannot be represented by a single valued function. It can be represented by implicit function x^2 +y^2=1, but if you try to express y in terms of x, equation splits into two: y1 = sqrt(1-x^2), y2 = -sqrt(1-x^2), representing "high" arc and "low" arc of the circle, respectively. Circle is a double valued function inherently. On the other hand, you can represent it as parametric function: y=sin fi, x=cos fi. The trick here was representing that logo as a set of parametric equations, and then using Fourier series to approximate them, not an original graph, which is multi valued.

@nanamacapagal8342 4 жыл бұрын

@@Hexanitrobenzene oh so that's what you meant by multivalued Sorry my brain was a bit fuzzy when I wrote that comment

@TheBasketBall13Freak 5 жыл бұрын

Destin, I want you to know how much of an inspiration you are to me. Every time I see a video of yours pop up I instantly feel so happy. These past few months have been a huge struggle for me. Just 15 minutes ago I was feeling so down and unmotivated but once I saw your video on my feed... I don't know how to explain it, but I just felt this instant relief for some reason. I feel happy and motivated now and it's all thanks to you. I hope you have a wonderful day. Great video!

@swacademy 4 жыл бұрын

Omg! This is one of the best things I've watched on KZfaq!! Thank you.

@Mayyde 3 жыл бұрын

I noticed a pretty interesting thing at around 6:40 So I do a TON of vector animation professionally, and I immediately recognized the way that the harmonic "wipers" were slowly assembling all of the correct curves to form the image. That's EXTREMELY SIMILAR to how Adobe Flash/Animate actually render the individual lines that are drawn with the brush. Back in the Flash 8 days, I imagine that the way Flash would render brush strokes would be taking the raw pixel data and try to recreate the curves using the fourier series in a similar way to how Doga drew the Smarter Every Day logo. Flash has the same type of behavior when you attempt to draw a really long stroke with lots of curves in it. Adobe changed Flash to Animate, and upgraded the brush so now it follows your input really closely with a ton of accuracy. I've noticed a significant change, and now that the lines have become extremely smooth, the actual time taken to render each stroke is quite long. That might mean that they're calculating the stroke with a ton of harmonics so that the strokes get REALLY SMOOTH, but now becomes more demanding on performance.

@mrwatney3236 5 жыл бұрын

After years of learning Fourier series in college now I know why it is important. Thanks Destin.

@enric898 5 жыл бұрын

This kind of things should be in the youtube rewind 2019

@Zetsuke4 5 жыл бұрын

Exactly

@kirtisawant9288 5 жыл бұрын

Yesssssss!

@duckymomo7935 5 жыл бұрын

Math YT is a subculture

@PerryCodes 3 жыл бұрын

"We can approximate anything as long you have enough terms." That right there is what makes mathematics so beautiful!!

@tailund3508 Жыл бұрын

Mind blowing, drawing that logo with a Fourier! Thank you! And a special thanks to Doga. That totally made it click for me as well. I must've watched >90% of your videos, and only now I realize you have a podcast.. Im really happy you do, though, and I subscribed immediately.

@EngineerPrepper 5 жыл бұрын

Ahhhhhhhhhhhhhhhhh... I finally get it after years of graduating college.

@Astro-wj2ro 5 жыл бұрын

ikr?

@demef758 5 жыл бұрын

Join the club!

@Mister_Soyuz_on_YT 5 жыл бұрын

Welp! I guess you are not forever a loan.

@aditsu 5 жыл бұрын

This visualization (which I've seen a couple of years ago) is cool but doesn't help me that much. I think what helped me the most to understand Fourier series is Winamp and its visualizations (in the 90's), combined with learning how to generate sampled sound from basic notes, and playing with an FFT algorithm. I still don't fully understand Fourier series.

@FactsNoFictions 5 жыл бұрын

It's very unfortunate that nobody in our uni never attempted to discuss the reasons for Fourier series to appear. As a student I've felt lost as what the heck this whole thing is about

@joshwarner5676 5 жыл бұрын

This is beautiful. Such a cool visual representation. It definitely would have helped me to see this when I was learning fourier series in calculus

@connorsturgeon8863 Жыл бұрын

it's cool revisiting some of destin's old content as I progress further into my engineering degree. i first watched this vid in high school, and the idea of fourier series seemed like peak math, phd level stuff, and now that I'm in my junior year, the mathematics behind fourier series is relatively simple, but visualizing it is still as magical as it was when I first learned about it 4 years ago

@Lightbulb909 4 жыл бұрын

I was smiling in amazement the whole time: I can watch this video for eternity!

@whyaskmenoely25 5 жыл бұрын

This concept is the key to sound design and synthesis. It's mindblowing knowing that all it takes is sine waves to emulate a real sound or make a sound you've never heard before.

@salih8566 5 жыл бұрын

I love that when you give the sources you use at details :)

@morganblarue Жыл бұрын

Fascinating. I exercise to your videos and time flies. It’s so fun.

@denislee5715 3 жыл бұрын

Thanks a lot for making this video and the animation. It does help me a lot in understanding how a series of sine waves can be resulted in a square wave. Really thanks a lot.

@MotorGoblin 5 жыл бұрын

7:48 "Makes a great gift." Don't you mean "jift"?

@tofu_golem 5 жыл бұрын

I have a very nice jrafics card in my computer.

@bcubed72 5 жыл бұрын

"Choosy programmers choose .gif!"

@adraedin 5 жыл бұрын

dude... i scrolled down to make this comment and you'd beaten me to it. have a thumbs up.

@coffeewind4409 5 жыл бұрын

When you use a pun about peanut butter to dictate how to pronounce a word

@Ely-ih5oy 5 жыл бұрын

Being second-language myself, I only knew it's pronounced "jif" from this video!!! like wtf

@poutouellet 5 жыл бұрын

This will revolutionalize the way Fourier series are explained in classes!

@BokrosD 3 жыл бұрын

That is fantastic! I really appreciate what you do! I am not well educated and I am not a mathematician, but I thoroughly enjoy the way you take complex ideas and break them down. Keep doing what you are doing!

@danielh9269 4 жыл бұрын

Amazing helpful visual demonstration. Thank you!

@krimpymess 5 жыл бұрын

As a musician and a synth addict who understands how adding mere sine waves atop another produces different textural sounds, this video makes me excited.

@felixftv8180 5 жыл бұрын

This is one of the most mind blowing videos I've seen about math

@dipalguha5599 4 жыл бұрын

Felix FTV

@ertugrul-bektik 4 жыл бұрын

Thanks for you and Doğa. Love from Turkey 🇹🇷🇹🇷

@dharvindaranarumugam3355 2 жыл бұрын

I'm studying Fourier series in Differential Equation. This video really help me to understand and also have a good visualization to understand that how sine waves produces in different waves shape . Thank you...

@sherlock_norris 5 жыл бұрын

Mathologer made a video explaining this with even more in depth math, if anyone is interested. He analyzes a function that can draw Homer Simpson.

@BrandenAllen 5 жыл бұрын

kzfaq.info/get/bejne/p7lke5mBqsmnc3U.html

@3blue1brown 5 жыл бұрын

It's really great! Highly recommended.

@ajsdoa6282 5 жыл бұрын

Yeah AND BTW 3BLUE1BROWN ALSO HAS A GREAT VIDEO ON THIS TOPIC AS WELL, GO CHECK THAT OUT! XD

@mienzillaz 5 жыл бұрын

Saw ML earlier than this.. anyway i would like to have this as a toy.. a physical thing, gears i ca reconfigurate

@downthecrossairs 5 жыл бұрын

I never comment on any videos but I just had to for this video.. I remember doing Fourier Series in my dorm, using Matlab and I am absolutely struggling with Fourier Series and am having the absolute worst time trying to plot them, then one of my roommates who is studying physical therapy (the highest math he took was college Algebra) walks in and goes "ohh that's 'just' a line graph". Never been so mad in my life, had to forward this video to him.

@danbahadurgurung8593 5 жыл бұрын

teach him some lesson . lol . make him realise his major is comic infront of pure mathematics

@arthurmead5341 5 жыл бұрын

He was right

@easyidle123 5 жыл бұрын

@@arthurmead5341 u wot

@jamiebeamguard4388 5 жыл бұрын

Ahh yes, beautiful MatLab

@thomash4578 4 жыл бұрын

@@danbahadurgurung8593 that attitude is one of the things wrong with academics. One field of study is not better than another. I am sure there are aspects of PT that would confuse a mathematical major.

@EricPalmer_DaddyOh Жыл бұрын

Destin, your videos are so fabulous. This is so beyond me. I understand the drawing part in concept only. But when I took physics I, we used slide rules and in physics II we used the brand new HP 35 calculator.

@NandishPatelV 2 жыл бұрын

WoW. I'm not a mathematician and have been trying to understand and visualise the Fourier series. Got it now! Thanks! KeepSmiling 😊🌺 I like the kids kit too. Will try it.

@deltaecho1 5 жыл бұрын

oh man ... somebody explained it to me finally in simple terms. Thank you!

@Soulsphere001 5 жыл бұрын

This actually reminds me of something I've recently started wondering about Adobe Illustrator. The whole objects orbiting other objects, which is what he's doing here. Or, more specifically, vertexes orbiting other vertexes.

@danielarco8566 3 жыл бұрын

It's so amazing and simple at the same time!Thanks,guys!

@hansangb 3 жыл бұрын

@0:48. Ahhhh the green grid paper. While I was visiting a book store for my son's college tour, I *had* to pick up a pack. It's been thirty years, but boy did it bring back memories!!!!! Everyone else thought it was weird, but I bet every engineering can commiserate and understand the nostalgia.

@pat2rome 5 жыл бұрын

As a synthesizer nerd, seeing this video pop up made me so happy. EDIT: and as a Georgia Tech grad, so did watching it!

@Wulfcry 5 жыл бұрын

Ahaah dare I say it if I'm guessing right FM synthesis.🤓

@AsyrafHalim 5 жыл бұрын

We apply this on vibration analysis, the time waveform, which also can be transformed into frequency spectrum via fast fourier transform (FFT)

@terryrogers6232 3 жыл бұрын

I went to undergrad school in archaic times when the lab "desktop" computer had a thick cable to a big hot box under the table. We did Fourier on this machine but glowing 'nixie' tube readout did not give you a solid feeling about it. Therefore, we were required to make a 1st + 3rd + 5th harmonic approximation of a square wave using free running sine signal generators stacked on top of each other with a signal combining network output to an oscilloscope. It was maddening to hold them stable enough at low frequencies so we could take a picture for the lab report. Fourier series has some limitations representing impulses but can be extended using the integral form (infinite number of frequencies in any interval which is more useful than it sounds) and windowing...multiplying the function to be approximated by a function 'window' like an exponential before doing Fourier analysis. I don't think there are many instructors who can seat the concept firmly in a students mind so that, for example, the student is not flabbergasted to find LaPlace transforms can solve physical system time behavior but also reveal the frequency response at the same time. They don't see this method as a form of Fourier analysis (and maybe missed the superposition idea). Anyway, it's easier to use SPICE computer network analysis...and I do. Very nice video indeed!

@rodrigoavilalarriva 4 жыл бұрын

Very easy to visualise!!. It took me lot of effort when I was student to understand what here seems so simple. Thanks and congratulations

@SthamerAMVs 5 жыл бұрын

Pretty useful video considering I’m about to start this at uni aha cheers man👍🏻

@smartereveryday 5 жыл бұрын

Nail it.

@SthamerAMVs 5 жыл бұрын

SmarterEveryDay will do my best:) cheers man, ps big fan😁

@willfrank961 5 жыл бұрын

Definitely check out 3blue1brown 's video on the furier transform. Super helpful!!

@SthamerAMVs 5 жыл бұрын

Will Frank already got it lined up! Cheers though:)

@jackgraffi160 5 жыл бұрын

I would like to see the function written out for the smarter everyday logo

@DiapaYY 5 жыл бұрын

A function can only have one y-value for every x-value so it's not possible to write it as a function (afaik)

@AvoidTheCadaver 5 жыл бұрын

@@DiapaYY That's not true. A parabolic or other even order polynomial function has 1 value of y for 2 or more values of x. Also multiple values of x in a sinusoidal function can return the same y value.

@SammzProductions 5 жыл бұрын

@@DiapaYY The functions of the x-coordinate(s) of the planar curve, as well as the y-coordinate(s) can definitely be written out. When combined, you have something called a vector-valued function. However, you would probably need a lot of paper to write out a good approximation.

@CatNolara 5 жыл бұрын

There are different kinds of functions, most people only know about y=f(x) (if they know about functions at all), but there are also parametric functions like x=f1(t) and y=f2(t), so the coordinates aren't dependent on eachother, but on a third value t that isn't a coordinate (you could look at it as "time" for example). Then you can define both functions and draw any curve you like, even with mutlipley values for the same x value. That's also what was done here. the functions for fourier functions usually look like this: x = f(t) = a0 + a1*sin(ωt) + a2*sin(2ωt) + ... b1*cos(ωt) + b2*cos(2ωt) + ... Every additional step adds another pair of sine and cosine terms.

@JiveDadson 5 жыл бұрын

@@DiapaYY The "y value" in this case is a complex number. Indeed, the Fourier transform is inherently in the complex domain. If he did it the way he did the real valued examples, the vertical axis is the real part. The reverse of that might be a more common convention.

@mezzoedbey3802 4 жыл бұрын

As an EEE student, I totally loved your video Keep up the good work 😊

@jamesbonanno3359 4 жыл бұрын

Wow that was absolutely amazing! I haven't seen something on KZfaq that caught my interest so well in a long time. I subscribed and I hit the Bell.

@jesshorowitz3308 5 жыл бұрын

Watching this instead of studying for the diff eq final tomorrow haha. Great visualization and I'm so glad I could kind of understand it after this semester! The SmarterEveryDay drawing function reminds of some kind of CNC laser cutting/milling program. Are fourier series, or something similar, used for vectoring?

@GerbenWijnja 5 жыл бұрын

4:22 "it's actually gif" Well, the g stands for 'graphics' (Graphics Interchange Format) so the g should be pronounced as in graphics... the Turkish guy pronounced it correctly.

@exnihilodub 5 жыл бұрын

but you pronounce PC as "pee-see" not "pee-kee" right? oh btw I'm not a fan of calling them "jeefs" either.

@werk62 5 жыл бұрын

The U in SCUBA stands for 'Underwater' but you don't pronounce it 'Sc-uh-ba'

@ozansahin97 5 жыл бұрын

he is saying like "graphics g" but in turkish language its pronounced also "graphics g" and i guess he is call it "graphics g " because of that

@jankoch267 5 жыл бұрын

It's an acronym so the creator decides how it should be pronounced and Steve Wilhite called it as Destin said. ;)

@mvmlego1212 5 жыл бұрын

In the words of the format’s creator, “choosey programmers choose gif”. It’s pronounced like the peanut butter brand.

@jameswebb8162 4 жыл бұрын

That’s absolutely rad dude!! I’m still wrapping my brain around it but dand it’s cool!!! Keep them coming!!!

@mmortazav 2 жыл бұрын

Dude, I never understood Fourier series in college but this video did the job. Hats off dustin, you are the best. (and obviously the genius in this video)

@HiVoltish 5 жыл бұрын

This stuff nearly split my head. This guy is amazing. Well done sir, well done.

@Trance_ 5 жыл бұрын

This takes me back to highschool Engineering class. We drew so many circles. So. Many. Circles.

@Blox117 5 жыл бұрын

do not disturb my circles!

@danimal_1814 Жыл бұрын

Love this ... just finished a master's degree and had some of this math in a "controls course" ... this is your best video ever. greetings from Switzerland. Hats off to Doga and your video channel. Daniel