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

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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/
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10 дек 2018

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Комментарии : 5 тыс.   
@benschofield1361
@benschofield1361 5 лет назад
Holy cow, Destin how are you today?
@smartereveryday
@smartereveryday 5 лет назад
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
@benschofield1361 5 лет назад
@@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
@Discostew2 5 лет назад
@@smartereveryday loved the podcast Destin, had me dying of laughter while you shared the pee story.
@Blox117
@Blox117 5 лет назад
@@smartereveryday get back to work, bot! who told you that you could pause making videos?! lol
@Chrisamic
@Chrisamic 5 лет назад
@@Discostew2 I haven't listened to the podcast yet, but I think I know where this is going LOL.
@TheCodingTrain
@TheCodingTrain 5 лет назад
Well, I guess I know what I'm going to try to program on this Friday's live stream!
@owendeheer5893
@owendeheer5893 5 лет назад
Well, I guess i know what I'm going to be watching on Friday!
@MisterDerban
@MisterDerban 5 лет назад
please do !!
@noxabellus
@noxabellus 5 лет назад
I was just thinking of you! This is a perfect match for your show :D
@markoftheland3115
@markoftheland3115 5 лет назад
Destin: "How did you make it?" Me: "processing? p5js?" Doga: no Me: :(
@plor1261
@plor1261 5 лет назад
I guess I know who I'm subbing to next!
@lbmetei7596
@lbmetei7596 4 года назад
Big fan of Mr. Fourier. He made my life very difficult.
@vishnubharathit6192
@vishnubharathit6192 4 года назад
LOL
@samamani5423
@samamani5423 4 года назад
:))))))))))
@VoidHalo
@VoidHalo 4 года назад
Yes, but without him, you wouldn't be watching this.
@sanamazarniya8092
@sanamazarniya8092 4 года назад
looooool
@riseabovehate9476
@riseabovehate9476 4 года назад
@@VoidHalo lol
@AsianBrozGaming
@AsianBrozGaming 4 года назад
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
@darshandabrase3265 4 года назад
Hey, you stole my thought.
@no_t1es
@no_t1es 4 года назад
_sad cosine noises_
@gamingbloopers6055
@gamingbloopers6055 4 года назад
Rerin YL dude, stop ruining the fun with your facts
@XenoghostTV
@XenoghostTV 4 года назад
@Rerin YL You don't say?
@jarvisluo5723
@jarvisluo5723 4 года назад
@@gamingbloopers6055 it's true tho. It's a flawed joke cuz it's not based on facts. That's not ingenious nor fun.
@akuljamwal3085
@akuljamwal3085 3 года назад
Dr. Doga hasn't looked happy since his pronunciation of GIF was corrected
@atlas_19
@atlas_19 3 года назад
LMFAO
@yashrohatgi6053
@yashrohatgi6053 Год назад
Ya see Norm, GIF stands for Giraffe Interchange Format, so it has to be pronounced that way...
@arnaudsimon3265
@arnaudsimon3265 Год назад
Ahahaha so true
@cchollands
@cchollands Год назад
Even ChatGPT agrees that the hard G pronunciation is more common. Take that, Destin.
@smartereveryday
@smartereveryday 5 лет назад
"It looks like a whip".... (Starts studying whips)
@charadremur333
@charadremur333 4 года назад
@@DemirSezer not no more. But yeah.
@charadremur333
@charadremur333 4 года назад
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
@michaelrose93 4 года назад
Whips have all sorts of uses...
@domainofscience
@domainofscience 5 лет назад
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
@TrentSheather 5 лет назад
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
@massimookissed1023 5 лет назад
Ima gonna hazard a guess that it sounds awful.
@Blox117
@Blox117 5 лет назад
it would sound like noise
@Blox117
@Blox117 5 лет назад
@@TrentSheather any type of wave can be considered "sound" not just a pure sine wave.
@MartinBuzon
@MartinBuzon 5 лет назад
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
@jerrygundecker743
@jerrygundecker743 4 года назад
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.
@sef83
@sef83 Год назад
Doga (Doğa, more correctly) means "nature" in Turkish. So "nature" tries to understand "nature" by using math :) proud of him!
@EAHowe
@EAHowe 5 лет назад
I had Dr. Doga for my Physics I and II classes my freshman year. Crazy to see him on this channel.
@Johnquistador
@Johnquistador 5 лет назад
Same here buddy
@egemenbags5465
@egemenbags5465 4 года назад
Which college is it
@andrewkarsten5268
@andrewkarsten5268 4 года назад
Egemen Bağış he said tech
@LetsbeHonest97
@LetsbeHonest97 3 года назад
@@egemenbags5465 Georgia Tech
@zeynabrahmani2248
@zeynabrahmani2248 2 года назад
How can we keep in touch with Doga?
@lauraleeane
@lauraleeane 5 лет назад
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
@bennytyty 5 лет назад
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
@ScormGaming 5 лет назад
You need to watch 3Blue1Brown's visualization of the Fourier transform.
@naonao77090
@naonao77090 2 года назад
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.
@TrevorHammonds
@TrevorHammonds 4 года назад
Your channel is truly one of RU-vid's gems. Keep up the terrific work!
@sunscream8502
@sunscream8502 5 лет назад
RU-vid should recommend these types of videos to everyone.
@Aemilindore
@Aemilindore 5 лет назад
it did!
@ov3rkill
@ov3rkill 5 лет назад
Instead they push their algorithm towards flat earth. lmao.
@gabrieldoudna6570
@gabrieldoudna6570 5 лет назад
ben shapiro wants to know your location
@mrzoldik201
@mrzoldik201 5 лет назад
@@ov3rkill it's fact , earth is flat
@neocortexlab
@neocortexlab 5 лет назад
@@ov3rkill that`s becouse the earth is realy flat in the place where youtube office is
@4rchfi3nd_4ct1ve
@4rchfi3nd_4ct1ve 5 лет назад
In Physics we have a saying: If you have one problem needs to be solved with fourier series, then you have 2 problems.
@wsjacksonjr
@wsjacksonjr 5 лет назад
Imagine how hard it would be then with a sevenier series!
@adamvav2730
@adamvav2730 5 лет назад
Mr. Jackson I like you
@alexanderstohr4198
@alexanderstohr4198 5 лет назад
fourier => frequency analysis - just pick the standard modules from the shelves if you are having to do it...
@corgikun2579
@corgikun2579 5 лет назад
@@wsjacksonjr your last name brings me nightmares (Classical Electrodynamics book by Jackson)
@nazishahmad1337
@nazishahmad1337 5 лет назад
@@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
@cakcakstudio7551
@cakcakstudio7551 2 года назад
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
@marcpaul8245 4 года назад
Finally, thanks to you, Destin, and Doga, I can visualize additive functions with a Fourier series! Thank you!
@SpaceSnaxxx
@SpaceSnaxxx 5 лет назад
4:23 "I made this amazing art tool and you're correcting my pronunciation?"
@we4selradio591
@we4selradio591 5 лет назад
Graphics Image Format. why would it be Jif? we don't say jraphics.
@Trias805
@Trias805 5 лет назад
@@we4selradio591 This
@commanderoof4578
@commanderoof4578 5 лет назад
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
@Novumic 5 лет назад
@@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
@Anon54387 5 лет назад
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.
@joescott
@joescott 5 лет назад
He says "gif". I like him.
@NautilusGuitars
@NautilusGuitars 5 лет назад
Fancy seeing you here!
@iankelk
@iankelk 5 лет назад
Joe Scott and Destin corrected him to gif and I don’t know how to feel. Btw it’s pronounced “gif”
@garydunken7934
@garydunken7934 5 лет назад
Very appropriate, because he is gif-ted.
@TheStaffmaster
@TheStaffmaster 5 лет назад
@@NautilusGuitars THERE'S DOZENS OF US!!! :p
@lambdastudios4083
@lambdastudios4083 5 лет назад
Its Gif, with a hard G. It Fundamentals book agrees with me
@mm-qd1ho
@mm-qd1ho Год назад
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!
@sodiboo
@sodiboo 2 года назад
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!
@jima1135
@jima1135 5 лет назад
His reaction to your correction of how to pronounce "gif" was perfect lol
@SomeDumDum01
@SomeDumDum01 5 лет назад
Jif
@abhinavgupta9990
@abhinavgupta9990 5 лет назад
It's not gif, it's gif.
@MouseGoat
@MouseGoat 5 лет назад
@@SomeDumDum01 gif gif gif, to the day i die! the internet was build on gifs... not jifs :D
@XypherOrion
@XypherOrion 5 лет назад
@@SomeDumDum01 Irrefutable proof that its a hard G, you have to spell it with a j to get the idea across. XD
@victorqwilleran3331
@victorqwilleran3331 5 лет назад
@@MouseGoat giraffe, ginger, German, gif.
@jaidenboucher0
@jaidenboucher0 5 лет назад
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
@AlexanderBukh 5 лет назад
so true
@Rujenz7
@Rujenz7 4 года назад
Welcome to the comment section, where we have: 90% about the GIF pronunciation 10% regarding the Fourier series
@triplea7071
@triplea7071 4 года назад
I know right
@adisuresh7263
@adisuresh7263 4 года назад
In which category should we classify your comment lol
@mophab
@mophab 2 года назад
Destin opened the can of worms by commenting about it. If he had let it pass, people wouldn't comment.
@TitoTheThird
@TitoTheThird 5 лет назад
2:35 Those "wipers" are called "epicycles" in Ptolemaic astronomy.
@verwehtverweht9053
@verwehtverweht9053 5 лет назад
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
@trevorjaster4072 5 лет назад
How are they used in astronomy
@verwehtverweht9053
@verwehtverweht9053 5 лет назад
@@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
@TitoTheThird 5 лет назад
@trevor: Epicycles were used to explain retrograde (or backwards) motion of the other planets in the Earth-centered Ptolemaic astronomy.
@lbblackburn
@lbblackburn 5 лет назад
And now the phrase "adding epicycles" generally means to make some theory work by adding absurd complexity.
@Freizeitflugsphaere
@Freizeitflugsphaere 5 лет назад
This is what kills me at university at the moment...
@TF23DayRespawn
@TF23DayRespawn 5 лет назад
I took PDEs about a year ago, ughhh that class was a pain, good luck!
@edeneden97
@edeneden97 5 лет назад
Watch 3b1b video on it
@willfrank961
@willfrank961 5 лет назад
Just echoing Eden's comment: 3blue1brown has an excellent video on the furier transform here on youtube.
@Freizeitflugsphaere
@Freizeitflugsphaere 5 лет назад
@@willfrank961 Thank's guys!😅
@Mickyleitor
@Mickyleitor 5 лет назад
Me too, Im doing it for the second time 😅
@clancybenedict6647
@clancybenedict6647 4 года назад
First SmarterEveryDay video I've seen and even the promo was cool lol. This is amazing. Subscribed
@richardsteen4340
@richardsteen4340 2 года назад
It is truly a great visualization to see how stacking/mixing sine waves actually produces different wave shapes.. Too cool..!! Love your Channel..!!
@TheBasketBall13Freak
@TheBasketBall13Freak 5 лет назад
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!
@Hexanitrobenzene
@Hexanitrobenzene 5 лет назад
"...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
@blancaroca8786 4 года назад
Here too. I am really annoyed with myself for not knowing about doing Fourier representation in 2d like that.
@nanamacapagal8342
@nanamacapagal8342 4 года назад
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
@Hexanitrobenzene 4 года назад
@@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
@nanamacapagal8342 4 года назад
@@Hexanitrobenzene oh so that's what you meant by multivalued Sorry my brain was a bit fuzzy when I wrote that comment
@AmericanPeasantry
@AmericanPeasantry 4 года назад
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!
@Mayyde
@Mayyde 3 года назад
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.
@harrymoschops
@harrymoschops 5 лет назад
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
@JiveDadson 5 лет назад
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
@OF01975 5 лет назад
Bullshit
@chandrakiranyada2253
@chandrakiranyada2253 4 года назад
I've used fourier series in numerical methods but this video made my mind blow away...brilliant.
@gumball1216
@gumball1216 3 года назад
Doga's face when you said jif had me in tears
@kennethduncan4643
@kennethduncan4643 3 года назад
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.
@DrTWG
@DrTWG 5 лет назад
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
@thehotdogman9317 3 года назад
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
@CammaProjects 3 года назад
Also add the starting phase of each harmonic sin(wt+phi1) + sin(3wt+phi3)/3 + sin(5wt+phi5)/5 ecc
@lukasmodry196
@lukasmodry196 Год назад
I love it, my teacher from algorithms first told me about this and i am absolutly amazed. Keep going!!!
@nicole-secondaryemail-mort9617
@nicole-secondaryemail-mort9617 4 года назад
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!
@FruitNBootNJordN
@FruitNBootNJordN 5 лет назад
“This transcends language” 😭😭😭 👌🏼💯 this was that cool, love it!
@Jimanator
@Jimanator 5 лет назад
3blue1brown and Mathologer both have wonderful videos on this subject
@thesaltedlamp3444
@thesaltedlamp3444 3 года назад
This was incredible! I can actually, finally, visualize the usefulness of, and the mathematics behind Fourier math!
@tailund3508
@tailund3508 Год назад
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.
@LivetoshootNC
@LivetoshootNC 5 лет назад
Wow. I wish we had visualizations like this when I was in school. These videos must inspire young engineers and science students.
@joshwarner5676
@joshwarner5676 5 лет назад
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
@jacksonmorris-thring644
@jacksonmorris-thring644 3 года назад
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!
@ponyote
@ponyote 2 года назад
The look you got for the correct pronunciation of gif (thank you!) that was blistering. You rock, Destin.
@apeters8
@apeters8 5 лет назад
Just want to point out that he's not a student! He's Dr. Doha!
@GoogleModerator
@GoogleModerator 5 лет назад
We are all students of science. Okay, I had to :)
@chaka5199
@chaka5199 4 года назад
Dr. Doha. Thank you.
@lukenelson556
@lukenelson556 4 года назад
Doga, with a G according to the video
@gokaytaspnar1355
@gokaytaspnar1355 4 года назад
its Doğa
@salih8566
@salih8566 5 лет назад
I love that when you give the sources you use at details :)
@connorsturgeon8863
@connorsturgeon8863 Год назад
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
@denislee5715
@denislee5715 3 года назад
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.
@Ozzah
@Ozzah 5 лет назад
I pronounce it "ga-jif" to make sure I cover all my bases.
@ZardoDhieldor
@ZardoDhieldor 5 лет назад
How to annoy every geek with only one word.
@winsauceiswin
@winsauceiswin 5 лет назад
Brilliant, I’m going to use this 😂😂😂
@IvarHuisman
@IvarHuisman 5 лет назад
Jyff is also a good one it approximates the spelling as a word G I F JYFF
@part-timepartytime9621
@part-timepartytime9621 5 лет назад
Zhaiff for life! Zhaiff for life! Zhaiff for life!
@KingBobXVI
@KingBobXVI 5 лет назад
"Gzheyf" - just to make sure it's wrong for everyone.
@XevianLight
@XevianLight 5 лет назад
That animation of making the SED logo with various instances of N should be your intro.
@alejo8alau
@alejo8alau 4 года назад
Cool idea
@ImXyper
@ImXyper 3 года назад
6:40
@morganblarue
@morganblarue Год назад
Fascinating. I exercise to your videos and time flies. It’s so fun.
@paulswanson3132
@paulswanson3132 4 года назад
You just BLEW my mind dude!! The simplest building blocks, like circles, can create ANYTHING!
@whyaskmenoely25
@whyaskmenoely25 5 лет назад
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.
@sherlock_norris
@sherlock_norris 5 лет назад
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
@BrandenAllen 5 лет назад
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-qS4H6PEcCCA.html
@3blue1brown
@3blue1brown 5 лет назад
It's really great! Highly recommended.
@ajsdoa6282
@ajsdoa6282 5 лет назад
Yeah AND BTW 3BLUE1BROWN ALSO HAS A GREAT VIDEO ON THIS TOPIC AS WELL, GO CHECK THAT OUT! XD
@mienzillaz
@mienzillaz 5 лет назад
Saw ML earlier than this.. anyway i would like to have this as a toy.. a physical thing, gears i ca reconfigurate
@swacademy
@swacademy 4 года назад
Omg! This is one of the best things I've watched on RU-vid!! Thank you.
@738polarbear
@738polarbear 4 года назад
I love watching smart people explain stuff . the smarter they are the humbler they seem to me.
@enumaelish11
@enumaelish11 5 лет назад
What a beauty! This video just explained a thing I'd been trying to understand, so thanks! Now I' a bit smarter :D
@quahntasy
@quahntasy 5 лет назад
This is such an intuitive way to understand Fourier series. Wish we were taught stuff in this way.
@lorenpearson1230
@lorenpearson1230 5 лет назад
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
@realedna 5 лет назад
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!!
@terryrogers6232
@terryrogers6232 3 года назад
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!
@danielh9269
@danielh9269 4 года назад
Amazing helpful visual demonstration. Thank you!
@mrwatney3236
@mrwatney3236 5 лет назад
After years of learning Fourier series in college now I know why it is important. Thanks Destin.
@krimpymess
@krimpymess 5 лет назад
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.
@ianchinsor9248
@ianchinsor9248 3 года назад
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
@jameswebb8162
@jameswebb8162 4 года назад
That’s absolutely rad dude!! I’m still wrapping my brain around it but dand it’s cool!!! Keep them coming!!!
@downthecrossairs
@downthecrossairs 5 лет назад
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
@danbahadurgurung8593 5 лет назад
teach him some lesson . lol . make him realise his major is comic infront of pure mathematics
@arthurmead5341
@arthurmead5341 5 лет назад
He was right
@easyidle123
@easyidle123 5 лет назад
@@arthurmead5341 u wot
@jamiebeamguard4388
@jamiebeamguard4388 5 лет назад
Ahh yes, beautiful MatLab
@thomash4578
@thomash4578 5 лет назад
@@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.
@jesshorowitz3308
@jesshorowitz3308 5 лет назад
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?
@Rondo2ooo
@Rondo2ooo 3 года назад
I can't recall the name of the YT clip, but there is a very nice explanation about digital to analogue square wave conversion when recording audio.
@BokrosD
@BokrosD 3 года назад
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!
@Soulsphere001
@Soulsphere001 5 лет назад
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.
@enric898
@enric898 5 лет назад
This kind of things should be in the youtube rewind 2019
@Zetsuke4
@Zetsuke4 5 лет назад
Exactly
@kirtisawant9288
@kirtisawant9288 5 лет назад
Yesssssss!
@duckymomo7935
@duckymomo7935 5 лет назад
Math YT is a subculture
@dharvindaranarumugam3355
@dharvindaranarumugam3355 2 года назад
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...
@leitecunha
@leitecunha 4 года назад
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 😄
@poutouellet
@poutouellet 5 лет назад
This will revolutionalize the way Fourier series are explained in classes!
@felixftv8180
@felixftv8180 5 лет назад
This is one of the most mind blowing videos I've seen about math
@dipalguha5599
@dipalguha5599 4 года назад
Felix FTV
@poly_hexamethyl
@poly_hexamethyl 4 года назад
Nice visualizations! So far, it shows the terms of the Fourier series and how they sum to approximate the target function. To take it a step further, I wonder if there is a way to visualize the systematic procedure by which the terms of the Fourier series are obtained from the original function?
@ertugrul-bektik
@ertugrul-bektik 4 года назад
Thanks for you and Doğa. Love from Turkey 🇹🇷🇹🇷
@jackgraffi160
@jackgraffi160 5 лет назад
I would like to see the function written out for the smarter everyday logo
@DiapaYY
@DiapaYY 5 лет назад
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
@AvoidTheCadaver 5 лет назад
@@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
@SammzProductions 5 лет назад
@@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
@CatNolara 5 лет назад
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
@JiveDadson 5 лет назад
@@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.
@MotorGoblin
@MotorGoblin 5 лет назад
7:48 "Makes a great gift." Don't you mean "jift"?
@tofu_golem
@tofu_golem 5 лет назад
I have a very nice jrafics card in my computer.
@bcubed72
@bcubed72 5 лет назад
"Choosy programmers choose .gif!"
@adraedin
@adraedin 5 лет назад
dude... i scrolled down to make this comment and you'd beaten me to it. have a thumbs up.
@coffeewind4409
@coffeewind4409 5 лет назад
When you use a pun about peanut butter to dictate how to pronounce a word
@Ely-ih5oy
@Ely-ih5oy 5 лет назад
Being second-language myself, I only knew it's pronounced "jif" from this video!!! like wtf
@PhysicsHigh
@PhysicsHigh 4 года назад
Thanks Destin - This has been really useful
@jamesbonanno3359
@jamesbonanno3359 4 года назад
Wow that was absolutely amazing! I haven't seen something on RU-vid that caught my interest so well in a long time. I subscribed and I hit the Bell.
@EricPalmer_DaddyOh
@EricPalmer_DaddyOh Год назад
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.
@deltaecho1
@deltaecho1 5 лет назад
oh man ... somebody explained it to me finally in simple terms. Thank you!
@danielarco8566
@danielarco8566 3 года назад
It's so amazing and simple at the same time!Thanks,guys!
@rodrigoavilalarriva
@rodrigoavilalarriva 4 года назад
Very easy to visualise!!. It took me lot of effort when I was student to understand what here seems so simple. Thanks and congratulations
@EngineerPrepper
@EngineerPrepper 5 лет назад
Ahhhhhhhhhhhhhhhhh... I finally get it after years of graduating college.
@Astro-wj2ro
@Astro-wj2ro 5 лет назад
ikr?
@demef758
@demef758 5 лет назад
Join the club!
@Mister_Soyuz_on_YT
@Mister_Soyuz_on_YT 5 лет назад
Welp! I guess you are not forever a loan.
@aditsu
@aditsu 5 лет назад
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
@FactsNoFictions 5 лет назад
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
@AsyrafHalim
@AsyrafHalim 5 лет назад
We apply this on vibration analysis, the time waveform, which also can be transformed into frequency spectrum via fast fourier transform (FFT)
@du.desouza
@du.desouza 3 года назад
This is one of the most amazing videos I've ever seen. Thank you!
@hansangb
@hansangb 3 года назад
@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.
@PerryCodes
@PerryCodes 3 года назад
"We can approximate anything as long you have enough terms." That right there is what makes mathematics so beautiful!!
@GerbenWijnja
@GerbenWijnja 5 лет назад
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
@exnihilodub 5 лет назад
but you pronounce PC as "pee-see" not "pee-kee" right? oh btw I'm not a fan of calling them "jeefs" either.
@werk62
@werk62 5 лет назад
The U in SCUBA stands for 'Underwater' but you don't pronounce it 'Sc-uh-ba'
@ozansahin97
@ozansahin97 5 лет назад
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
@jankoch267 5 лет назад
It's an acronym so the creator decides how it should be pronounced and Steve Wilhite called it as Destin said. ;)
@mvmlego1212
@mvmlego1212 5 лет назад
In the words of the format’s creator, “choosey programmers choose gif”. It’s pronounced like the peanut butter brand.
@beeflat4287
@beeflat4287 2 года назад
Bloomin´ facinating ! 😯😮😲 You inspired me. I might use this thought for my programming, thanks.
@NandishPatelV
@NandishPatelV 2 года назад
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.
@pat2rome
@pat2rome 5 лет назад
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
@Wulfcry 5 лет назад
Ahaah dare I say it if I'm guessing right FM synthesis.🤓
@SlowlyYouRot
@SlowlyYouRot 5 лет назад
I want this visualization on an oscillator synth module! Would make for a very cool design to interact with to make waveforms on a synthesizer.
@electronmechanicalcorporat2143
Just get one of those 30 dollar oscilloscope kits.
@SlowlyYouRot
@SlowlyYouRot 5 лет назад
@@electronmechanicalcorporat2143 I mean I want to see the circles and interact with them to make waveforms on a synth.
@mezzoedbey3802
@mezzoedbey3802 4 года назад
As an EEE student, I totally loved your video Keep up the good work 😊
@danimal_1814
@danimal_1814 Год назад
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
@mistervoldemort7540
@mistervoldemort7540 5 лет назад
4:27 "So if I were to GIF you a function" XD
@givanildogodinho7553
@givanildogodinho7553 4 года назад
"You could make a graph with this?" Wouldn't be "Could you..." since it is a question?