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.
@@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!
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.
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.
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.
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?
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.
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
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.
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 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.
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!
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.
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!
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.
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!!
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.
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.
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.
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 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.
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.
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!
"...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
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.
@@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.
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.
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
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.
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.
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.
@@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.
@@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.
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.
@@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.
6:19 I really love what u said there... "u may think it's a complete chaos, but it's not, it's complete ORDER" makes me think of how the universe is like.... people say particle in this huge boiling kettle we are livining is in complete chaos... uncertainity of where the particles are and will be... uncertainty & probability, but people don't realize that this uncertainty... emerge from the idea of how we are limited in observing these "uncertain" particles with a clear eye... but deep instead of how they particle behave there might be an order. , we just don't notice it or know about it. After all they probabilities them is government by mathematical functions which determines the particles con-straits and abilities?
thats not true with HUP. you can only know of the location or vector from measurement, you cannot know both as measurement causes it's state to flip. You're treating quanta with macro characteristics. The collapse changes instrinsic properties of the system. If you were to use wimp or bending constraints of instrinsic properties like spin states/ angular momentum/charge/mass or kinetic information, like the vector of the wave through the membrane the field occupies you would still be limited to the uncertainty principle, which isn't directly connected to psi superposition of combined spin or vectorstates. you would need to wimp measure it twice and after the first wimp state changes to find information out, you removed that information from the object and its not the same object as before it's a different state than originally. That would be like measuring a cat to find the location, then measuring a dog to find out something else about the cat somehow even though the dog doesnt have information about the cat. Thats QED for 1/2 spin integers. With QCD you have 6 colorstates and bosons to mediate pion and quarks. They have different properties for measurement than a 1/2 spin state where 360 degrees has different information than 0/720 degree state.
So, what is the Fourier series precisely, and i am interested in learning more about it? Thank you so much for everything. This is an easy-to-understand explanation.
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.
GIF is an acronym for graphic information file. The “G” is a hard “g”, such as get, grab, graphic, or great. A soft “g” is gel, genius, germ. Hence, gif is pronounced with a hard g (graphic) not a soft g (germ). Use a hard g. You’re welcome.
When I was in school the professors thought the future was with analog systems. LaPlace / Fourier transforms were in vogue then. I was in my senior year before I saw anything digital.
Yes, wanted to mention the Ptolemaic Epicycles and how they more accurately predicted the motion of the planets - until Laplace 250 years after Copernicus. In his multipart masterpiece, Mécanique Céleste, the first volume of which appeared in 1798, Laplace demonstrates that the solar system is stable over periods of time longer than Newton could predict. To do so, Laplace pioneered a new kind of mathematics called perturbation theory, which enabled him to examine the cumulative effects of many small forces.
All schools should stop looking at sine and cosine functions as " Flat" functions that can be drawn on a plane, as they miss one dimension of the many dimensions in which many functions do exist. Sine and Cosine, each consist of the summation or the subtraction of two three dimensional rotation in opposite directions. If one makes it clear that the flat pulsating sine and cosine are only the projection of a three-dimensional function, life for students engineers would be so much simpler. One should learn to visualize in three dimension e^( r+jwt) - e^rt*( cos( wt) + j.sin(wt) and the opposite rotation e^ rt *( cos( wt) -j.sin(wt) and one can see many beautiful images being created when handling Fourier, Laplace, Convolution Integrals and how filters operate with their impulse function operating on a kernel operating on an input signal. All this can be seen in three dimensions. Beautiful work indeed. When I was very young I did see all this and I am sure that Fourier and Laplace did mean to explain that all their work was meant to be understood as three-dimensional work............I believe what happened was that their audience did not understand what Fourier and Laplace really meant by their operators, and so the audience went around the world and they preached what they did not fully understand! Pity, such pity books are written describing sine and cosine as flat functions when their origin is from three-dimensional operations using three-dimensional rotating ( helical) functions
Can you provide any detailed references for the same? I understand using exponential notations for sine and cosine on the surface but the 2d projection thing and the implications of thinking about them in 3d are not really clear to me. Thanks in advance!
It would be interesting to use the golden ratio with the fibonacci sequence Like ratio the diameters 1.61803 but fibonacci the connection spacing 1,1,2,3,5,8,13,21 Might make something that resembles nature
These videos following the first year uni physics curriculum on purpose? Swear the last few videos have been on the subjects of my lectures and are released on the same day. It’s really useful...
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!
@@Forien Because all acronyms are pronounced exactly as you would expect based on their origin. Es-Cee-Es-I or scuzzy? (even if the gate-gif sounds more natural to me than the jive-gif (as a Dutch speaker of English), there is no reason your explanation would be written in stone)
Wow! I failed Fourier Transforms at third year electrical engineering. This would have got me through. Great work, now i'll look up Laplace Transforms. Failed that too.
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.
There are a lot of smart people in the world, even in America. 3% of 300 million is still a big number, even if 97% just want to watch trash like The Bachelor.
SETI (Search for Extra-Terrific Intelligence) actually whipped most of these guys up in the late 60s. But only recently has their existence been outed to the public. *I'm telling you, the government is bees, maaan! *
@@Hallowed_Ground SETI is supposed to stand for "the Search for ExtraTerrestrial Intelligence". It's a real organisation that keeps an ear (radio telescopes) to the sky. The more you know
Nothing transcends language; it is a protective barrier that we have foolishly weakened. But obviously this man has a gift that can make him a blessing to his people.
Yeah I used to say jif...but I came around when I realised the JPEG Interchange Format was a thing...like 20 years ago. I wonder how the Grrrr mans feel? :D
Dr. Doga used to be my professor at Georgia Southern!! Definitely the best professor I ever had. He came in to class one day with a microwave and cheese to prove the speed of light lol. He taught for understanding not just for abject knowledge.
Not to be douche but you can approximate a function as close as wanted with many types of functions not just sine functions. (Some examples are activation functions in machine learning: sigmoid, relu, tanh,step, etc.) but sine functions are periodic and so any wave can be broken down and represented as sine functions which makes the fourier transform significant
Hi Destin, I've thought about car windshield wipers since I was tiny. There are loads of kinds: single blades, double blades, double-joined single blades, etc. What's the best way to wipe a windshield so you don't get (or have the smallest) unwiped areas with the lowest number of blades? What's the shape of the unwiped areas: shark fins, archways, etc?
Marisa Lau if you’re ambitious, with a few modifications a single blade could probably wipe 100% of the windshield. Otherwise, having 2 conditions at the same time (smallest unwiped area AND smallest number of blades) makes this question mathematically impossible to answer, as you can try to minimize each variable separately (eg. 0% unwiped area, but would require more blades), but not both at the same time. Is 10% leftover area with 3 blades more or is it less than 7% leftover, but with 4 blades? It’s impossible to answer.
I'm a vibration analyst (predictive maintenance for rotating machines), and we use fast Fourier transform (FFT) to be able to more easily separate and view different vibration frequencies from a raw timewave form. I don't have an engineering background so I have no idea how the math works. But it's very cool to see different sides of Fourier in action
Old guys such as I, and computer geeks say "jiff", because that's how the inventor of the format says it. Young guys say "ghiff", because the g stands for "graphics." The inventor says he doesn't care one way or the other. So, take your pick and argue.
![กี่หมื่นฟ้า | Your Sky Series EP.1 [1/4]](http://i.ytimg.com/vi/vLGjxFL6U_I/mqdefault.jpg)
Holy cow, Destin how are you today?
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.
@@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!
@@smartereveryday loved the podcast Destin, had me dying of laughter while you shared the pee story.
@@smartereveryday get back to work, bot! who told you that you could pause making videos?! lol
@@Discostew2 I haven't listened to the podcast yet, but I think I know where this is going LOL.
Well, I guess I know what I'm going to try to program on this Friday's live stream!
Well, I guess i know what I'm going to be watching on Friday!
please do !!
I was just thinking of you! This is a perfect match for your show :D
Destin: "How did you make it?"
Me: "processing? p5js?"
Doga: no
Me: :(
I guess I know who I'm subbing to next!
Big fan of Mr. Fourier. He made my life very difficult.
LOL
:))))))))))
Yes, but without him, you wouldn't be watching this.
looooool
@@VoidHalo lol
I had Dr. Doga for my Physics I and II classes my freshman year. Crazy to see him on this channel.
Same here buddy
Which college is it
Egemen Bağış he said tech
@@egemenbags5465 Georgia Tech
How can we keep in touch with Doga?
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
Hey, you stole my thought.
_sad cosine noises_
Rerin YL dude, stop ruining the fun with your facts
@Rerin YL You don't say?
@@gamingbloopers6055 it's true tho. It's a flawed joke cuz it's not based on facts. That's not ingenious nor fun.
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.
If you haven't seen it yet, 3blue1brown is an amazing channel that's full of visualizations that show off the beauty of math.
You need to watch 3Blue1Brown's visualization of the Fourier transform.
TH-cam should recommend these types of videos to everyone.
it did!
Instead they push their algorithm towards flat earth. lmao.
ben shapiro wants to know your location
@@ov3rkill
it's fact , earth is flat
@@ov3rkill that`s becouse the earth is realy flat in the place where youtube office is
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.
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.
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?
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.
Ima gonna hazard a guess that it sounds awful.
it would sound like noise
@@TrentSheather any type of wave can be considered "sound" not just a pure sine wave.
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
"It looks like a whip".... (Starts studying whips)
@@DemirSezer not no more. But yeah.
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.
Whips have all sorts of uses...
Whips make a sonic boom i think, that's neat.
In Physics we have a saying: If you have one problem needs to be solved with fourier series, then you have 2 problems.
Imagine how hard it would be then with a sevenier series!
Mr. Jackson I like you
fourier => frequency analysis - just pick the standard modules from the shelves if you are having to do it...
@@wsjacksonjr your last name brings me nightmares (Classical Electrodynamics book by Jackson)
@@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
Dr. Doga hasn't looked happy since his pronunciation of GIF was corrected
LMFAO
Ya see Norm, GIF stands for Giraffe Interchange Format, so it has to be pronounced that way...
Ahahaha so true
Even ChatGPT agrees that the hard G pronunciation is more common. Take that, Destin.
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.
so true
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.
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.
Also add the starting phase of each harmonic sin(wt+phi1) + sin(3wt+phi3)/3 + sin(5wt+phi5)/5 ecc
He says "gif". I like him.
Fancy seeing you here!
Joe Scott and Destin corrected him to gif and I don’t know how to feel. Btw it’s pronounced “gif”
Very appropriate, because he is gif-ted.
@@NautilusGuitars THERE'S DOZENS OF US!!! :p
Its Gif, with a hard G. It Fundamentals book agrees with me
2:35 Those "wipers" are called "epicycles" in Ptolemaic astronomy.
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...
How are they used in astronomy
@@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.
@trevor: Epicycles were used to explain retrograde (or backwards) motion of the other planets in the Earth-centered Ptolemaic astronomy.
And now the phrase "adding epicycles" generally means to make some theory work by adding absurd complexity.
3blue1brown and Mathologer both have wonderful videos on this subject
Doga (Doğa, more correctly) means "nature" in Turkish. So "nature" tries to understand "nature" by using math :) proud of him!
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!
His reaction to your correction of how to pronounce "gif" was perfect lol
Jif
It's not gif, it's gif.
@@SomeDumDum01 gif gif gif, to the day i die!
the internet was build on gifs... not jifs :D
@@SomeDumDum01 Irrefutable proof that its a hard G, you have to spell it with a j to get the idea across. XD
@@MouseGoat giraffe, ginger, German, gif.
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.
Wow. I wish we had visualizations like this when I was in school. These videos must inspire young engineers and science students.
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!
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.
th-cam.com/video/qS4H6PEcCCA/w-d-xo.html
It's really great! Highly recommended.
Yeah AND BTW 3BLUE1BROWN ALSO HAS A GREAT VIDEO ON THIS TOPIC AS WELL, GO CHECK THAT OUT! XD
Saw ML earlier than this.. anyway i would like to have this as a toy.. a physical thing, gears i ca reconfigurate
This is what kills me at university at the moment...
I took PDEs about a year ago, ughhh that class was a pain, good luck!
Watch 3b1b video on it
Just echoing Eden's comment: 3blue1brown has an excellent video on the furier transform here on youtube.
@@willfrank961 Thank's guys!😅
Me too, Im doing it for the second time 😅
This is such an intuitive way to understand Fourier series. Wish we were taught stuff in this way.
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.
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!!
Your channel is truly one of TH-cam's gems. Keep up the terrific work!
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.
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.
Bullshit
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.
I've used fourier series in numerical methods but this video made my mind blow away...brilliant.
Thanks for you and Doğa. Love from Turkey 🇹🇷🇹🇷
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.
teach him some lesson . lol . make him realise his major is comic infront of pure mathematics
He was right
@@arthurmead5341 u wot
Ahh yes, beautiful MatLab
@@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.
That animation of making the SED logo with various instances of N should be your intro.
Cool idea
6:40
Welcome to the comment section, where we have:
90% about the GIF pronunciation
10% regarding the Fourier series
I know right
In which category should we classify your comment lol
Destin opened the can of worms by commenting about it. If he had let it pass, people wouldn't comment.
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.
I pronounce it "ga-jif" to make sure I cover all my bases.
How to annoy every geek with only one word.
Brilliant, I’m going to use this 😂😂😂
Jyff is also a good one it approximates the spelling as a word G I F JYFF
Zhaiff for life! Zhaiff for life! Zhaiff for life!
"Gzheyf" - just to make sure it's wrong for everyone.
Just want to point out that he's not a student! He's Dr. Doha!
We are all students of science. Okay, I had to :)
Dr. Doha. Thank you.
Doga, with a G according to the video
its Doğa
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!
7:48 "Makes a great gift." Don't you mean "jift"?
I have a very nice jrafics card in my computer.
"Choosy programmers choose .gif!"
dude... i scrolled down to make this comment and you'd beaten me to it. have a thumbs up.
When you use a pun about peanut butter to dictate how to pronounce a word
Being second-language myself, I only knew it's pronounced "jif" from this video!!! like wtf
Doga's face when you said jif had me in tears
"...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
Here too. I am really annoyed with myself for not knowing about doing Fourier representation in 2d like that.
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.
@@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.
@@Hexanitrobenzene oh so that's what you meant by multivalued
Sorry my brain was a bit fuzzy when I wrote that comment
I love it, my teacher from algorithms first told me about this and i am absolutly amazed. Keep going!!!
Ahhhhhhhhhhhhhhhhh... I finally get it after years of graduating college.
ikr?
Join the club!
Welp! I guess you are not forever a loan.
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.
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
This kind of things should be in the youtube rewind 2019
Exactly
Yesssssss!
Math YT is a subculture
This is one of the most mind blowing videos I've seen about math
Felix FTV
I love watching smart people explain stuff . the smarter they are the humbler they seem to me.
As a synthesizer nerd, seeing this video pop up made me so happy.
EDIT: and as a Georgia Tech grad, so did watching it!
Ahaah dare I say it if I'm guessing right FM synthesis.🤓
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.
"We can approximate anything as long you have enough terms." That right there is what makes mathematics so beautiful!!
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.
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.
but you pronounce PC as "pee-see" not "pee-kee" right? oh btw I'm not a fan of calling them "jeefs" either.
The U in SCUBA stands for 'Underwater' but you don't pronounce it 'Sc-uh-ba'
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
It's an acronym so the creator decides how it should be pronounced and Steve Wilhite called it as Destin said. ;)
In the words of the format’s creator, “choosey programmers choose gif”. It’s pronounced like the peanut butter brand.
I would like to see the function written out for the smarter everyday logo
A function can only have one y-value for every x-value so it's not possible to write it as a function (afaik)
@@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.
@@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.
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.
@@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.
6:19 I really love what u said there... "u may think it's a complete chaos, but it's not, it's complete ORDER" makes me think of how the universe is like....
people say particle in this huge boiling kettle we are livining is in complete chaos... uncertainity of where the particles are and will be... uncertainty & probability, but people don't realize that this uncertainty... emerge from the idea of how we are limited in observing these "uncertain" particles with a clear eye... but deep instead of how they particle behave there might be an order. , we just don't notice it or know about it. After all they probabilities them is government by mathematical functions which determines the particles con-straits and abilities?
thats not true with HUP. you can only know of the location or vector from measurement, you cannot know both as measurement causes it's state to flip. You're treating quanta with macro characteristics. The collapse changes instrinsic properties of the system. If you were to use wimp or bending constraints of instrinsic properties like spin states/ angular momentum/charge/mass or kinetic information, like the vector of the wave through the membrane the field occupies you would still be limited to the uncertainty principle, which isn't directly connected to psi superposition of combined spin or vectorstates. you would need to wimp measure it twice and after the first wimp state changes to find information out, you removed that information from the object and its not the same object as before it's a different state than originally. That would be like measuring a cat to find the location, then measuring a dog to find out something else about the cat somehow even though the dog doesnt have information about the cat. Thats QED for 1/2 spin integers. With QCD you have 6 colorstates and bosons to mediate pion and quarks. They have different properties for measurement than a 1/2 spin state where 360 degrees has different information than 0/720 degree state.
@@DerpMuse that's awesome!
So, what is the Fourier series precisely, and i am interested in learning more about it? Thank you so much for everything. This is an easy-to-understand explanation.
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 😄
This will revolutionalize the way Fourier series are explained in classes!
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.
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
I say 'gif' too. Jif is some sort of bathroom cleaner liquid.
sting aling *peanut butter intensifies*
GIF is an acronym for graphic information file. The “G” is a hard “g”, such as get, grab, graphic, or great. A soft “g” is gel, genius, germ. Hence, gif is pronounced with a hard g (graphic) not a soft g (germ). Use a hard g. You’re welcome.
@@davidgrubbs2334 i believe the person who made/popularised gif said that it was pronounced jif
Naverdo Sandeep That person, I believe, was mistaken.
@@davidgrubbs2334 my giraffe won't discuss it.
"You can represent any function"
Any L^2 function, specifically. It needs to have a finite norm in L^2 for Parseval's theorem to hold
When I was in school the professors thought the future was with analog systems. LaPlace / Fourier transforms were in vogue then. I was in my senior year before I saw anything digital.
Now everything is digital and tommorow, maybe, we will go quantum (which is neither digital nor analog - it contains both).
You just BLEW my mind dude!! The simplest building blocks, like circles, can create ANYTHING!
“This transcends language” 😭😭😭 👌🏼💯 this was that cool, love it!
oh man ... somebody explained it to me finally in simple terms. Thank you!
Well, even pre-Keplerian astronomers knew that you can approximate anything if you just use enough epicycles ;)
Haha, funny coincidence right?
Wait...
Yes, wanted to mention the Ptolemaic Epicycles and how they more accurately predicted the motion of the planets - until Laplace 250 years after Copernicus. In his multipart masterpiece, Mécanique Céleste, the first volume of which appeared in 1798, Laplace demonstrates that the solar system is stable over periods of time longer than Newton could predict. To do so, Laplace pioneered a new kind of mathematics called perturbation theory, which enabled him to examine the cumulative effects of many small forces.
And whats your point?
@@obeb787 My point is, you can do a heck of a lot with circles if you understand Ptolemy.
@@johnmiglautsch4587 lol, comment was not directed to you but on! Lol
Hey but now i know, i didn't know at all
The look you got for the correct pronunciation of gif (thank you!) that was blistering. You rock, Destin.
All schools should stop looking at sine and cosine functions as " Flat" functions that can be drawn on a plane, as they miss one dimension of the many dimensions in which many functions do exist. Sine and Cosine, each consist of the summation or the subtraction of two three dimensional rotation in opposite directions. If one makes it clear that the flat pulsating sine and cosine are only the projection of a three-dimensional function, life for students engineers would be so much simpler.
One should learn to visualize in three dimension e^( r+jwt) - e^rt*( cos( wt) + j.sin(wt) and the opposite rotation e^ rt *( cos( wt) -j.sin(wt) and one can see many beautiful images being created when handling Fourier, Laplace, Convolution Integrals and how filters operate with their impulse function operating on a kernel operating on an input signal. All this can be seen in three dimensions. Beautiful work indeed.
When I was very young I did see all this and I am sure that Fourier and Laplace did mean to explain that all their work was meant to be understood as three-dimensional work............I believe what happened was that their audience did not understand what Fourier and Laplace really meant by their operators, and so the audience went around the world and they preached what they did not fully understand! Pity, such pity books are written describing sine and cosine as flat functions when their origin is from three-dimensional operations using three-dimensional rotating ( helical) functions
Can you provide any detailed references for the same? I understand using exponential notations for sine and cosine on the surface but the 2d projection thing and the implications of thinking about them in 3d are not really clear to me. Thanks in advance!
Good points , but some edits to the formula are needed to correct errors including missing and wrong parentheses, = sign not - , etc .
bro u should watch fourier series explained by Physics video by eugene and also by 3blue1brown.Not just those watch their take on linear algebra too
As bayrakları as as as!
as kanka geliyorum. türklerin çogu yabancı müzik kliplerinde fink atıyor şuan :D
@@aliihsantopuz1069 muhtemelen öyle yapıyorlar
Kimler neler yapıyor keşke bende onlardan biri olabilseymişim
Gururlandık be👏🏻👏🏻🇹🇷🇹🇷🇹🇷
Vay be
It would be interesting to use the golden ratio with the fibonacci sequence
Like ratio the diameters 1.61803 but fibonacci the connection spacing
1,1,2,3,5,8,13,21
Might make something that resembles nature
I’m proud to say, after 5 years, when I finished the 3B1B Differential Equations Fourier Series course, I can finally understand this video.
This takes me back to highschool Engineering class. We drew so many circles. So. Many. Circles.
do not disturb my circles!
A 78-years old SWISS-boy says you: Fan-tas-tic! Thank you for this video!
"sagt dir" nur einen Hinweis auf Englisch würde man "tell" stattdessen "say" da nutzten
You are not alone, Hans. This 72 year-old had the same reaction!
This 52 year old Aboriginal Australian had the same reaction too. Hello from Australia : )
This spoiled 15 year old punk was blown away too.........
These videos following the first year uni physics curriculum on purpose? Swear the last few videos have been on the subjects of my lectures and are released on the same day. It’s really useful...
thats because we(you) live in a simulation
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!
Pretty useful video considering I’m about to start this at uni aha cheers man👍🏻
Nail it.
SmarterEveryDay will do my best:) cheers man, ps big fan😁
Definitely check out 3blue1brown 's video on the furier transform. Super helpful!!
Will Frank already got it lined up! Cheers though:)
We apply this on vibration analysis, the time waveform, which also can be transformed into frequency spectrum via fast fourier transform (FFT)
We gonna learn today....😀
Finally, thanks to you, Destin, and Doga, I can visualize additive functions with a Fourier series! Thank you!
Oh no Destin has shared his OPINION on the pronunciation of gif...
It isn't an opinion.
@Juho Leiniö gift, give, gigabyte...gif
@@user-de1xi2uf8d The creator said it was jif
@@JensenPlaysMC Google why he made that mistake
@@Forien Because all acronyms are pronounced exactly as you would expect based on their origin. Es-Cee-Es-I or scuzzy?
(even if the gate-gif sounds more natural to me than the jive-gif (as a Dutch speaker of English), there is no reason your explanation would be written in stone)
I was smiling in amazement the whole time: I can watch this video for eternity!
Wow! I failed Fourier Transforms at third year electrical engineering. This would have got me through. Great work, now i'll look up Laplace Transforms. Failed that too.
@shahzeb ali me during the first three years of my physics program.
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.
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.
Just get one of those 30 dollar oscilloscope kits.
@@electronmechanicalcorporat2143 I mean I want to see the circles and interact with them to make waveforms on a synth.
Finally, I've found intelligent life on TH-cam!
Unbelievable!
You should watch 3blue1brown channel
There are a lot of smart people in the world, even in America. 3% of 300 million is still a big number, even if 97% just want to watch trash like The Bachelor.
SETI (Search for Extra-Terrific Intelligence) actually whipped most of these guys up in the late 60s. But only recently has their existence been outed to the public.
*I'm telling you, the government is bees, maaan! *
@@pranavlimaye What? I get the last part of your comment is a joke but what arre you even saying in the rest of it?
@@Hallowed_Ground
SETI is supposed to stand for "the Search for ExtraTerrestrial Intelligence". It's a real organisation that keeps an ear (radio telescopes) to the sky.
The more you know
Wow wow wow 🤩...
How can we learn to do this for any shape we want????
Nothing transcends language; it is a protective barrier that we have foolishly weakened. But obviously this man has a gift that can make him a blessing to his people.
What a beauty!
This video just explained a thing I'd been trying to understand, so thanks! Now I' a bit smarter :D
When people start saying "jraphics", I'll start saying "jif".
Ahhh yes, when people start saying "potographic" I'll start calling it a "jpeg"
@@russellcroft9196 no correlation
Yeah I used to say jif...but I came around when I realised the JPEG Interchange Format was a thing...like 20 years ago. I wonder how the Grrrr mans feel? :D
@@yigitpolat Yes correlation 🥶
@@russellcroft9196 do you say jift instead of gift?
That's pretty extraordinary. I wonder what particular tone the "human head" sound wave possesses?
Now your speaking my language
Dr. Doga used to be my professor at Georgia Southern!! Definitely the best professor I ever had. He came in to class one day with a microwave and cheese to prove the speed of light lol. He taught for understanding not just for abject knowledge.
its not every day you learn something in engineering which destain has actually made a video about.
Not to be douche but you can approximate a function as close as wanted with many types of functions not just sine functions. (Some examples are activation functions in machine learning: sigmoid, relu, tanh,step, etc.) but sine functions are periodic and so any wave can be broken down and represented as sine functions which makes the fourier transform significant
How about a shout out to Chebyshev polynomials? I am a fan boy.
7:48 destin you said it wrong, it's actually "JIFT" I don't know if you knew that
LOL
jood one!
As an EEE student, I totally loved your video
Keep up the good work 😊
Hi Destin, I've thought about car windshield wipers since I was tiny. There are loads of kinds: single blades, double blades, double-joined single blades, etc. What's the best way to wipe a windshield so you don't get (or have the smallest) unwiped areas with the lowest number of blades? What's the shape of the unwiped areas: shark fins, archways, etc?
Marisa Lau if you’re ambitious, with a few modifications a single blade could probably wipe 100% of the windshield.
Otherwise, having 2 conditions at the same time (smallest unwiped area AND smallest number of blades) makes this question mathematically impossible to answer, as you can try to minimize each variable separately (eg. 0% unwiped area, but would require more blades), but not both at the same time. Is 10% leftover area with 3 blades more or is it less than 7% leftover, but with 4 blades? It’s impossible to answer.
This is when you realize how smart he is after all these days
0:42 how did you know that the second half of the curve (from 0 to pi) was a graph of sin(x) ?
You can see that at pi/2 the value of the curve is 1 and 0 at 0 and pi.
I'm a vibration analyst (predictive maintenance for rotating machines), and we use fast Fourier transform (FFT) to be able to more easily separate and view different vibration frequencies from a raw timewave form. I don't have an engineering background so I have no idea how the math works. But it's very cool to see different sides of Fourier in action
Old guys such as I, and computer geeks say "jiff", because that's how the inventor of the format says it. Young guys say "ghiff", because the g stands for "graphics." The inventor says he doesn't care one way or the other. So, take your pick and argue.
but I thought that it was pronounced like the g in garage.
toe-may-toe … toe-mah-toe.
@@ilanwallace2220 is it gaRAge or GArage?
@@treelinehugger po-tay-t....oh, forget it! ;-)
Thank Jod someone can jive us both the jift of jood background info AND a sensible attitude. Jet this man a beer!