Fourier Series Animation (Saw Wave)

[@BrekMartin]

An interesting one guys. This video didn’t get any attention for a few years! There’s a square wave version on my channel if you are keen to search it (since this has been asked). It’s silent though.

[@sebbes333]

Can you do the same, but match the graph to the Y-axis? just to see what pattern comes out that way too :D

[@policedog4030]

A challange is to close your eyes and run the animation in your minds eye. The first circle's radius begins at the three o'clock position and rotates counterclockwise. The waveform trace is written at a varying standoff distance of about the same as the radius. Then the second circle's radius begins at the three o'clock position but this one rotates clockwise. Good exercise for the brain and better than counting sheep when trying to sleep. I can't believe this video doesn't have tens of millions of views as I've come back to watch it lots of times

[@KENKENNIFF]

Its amazing that such a simple set of stable processes combine to create such a apparantly random pattern

[@marksmod]

it is good that the music is in sync with the period of the wave.

[@JaDanBar97]

Seeing how a fourier series works is super fascinating

[@Dazdingo]

Have you've seen Fouriers graphed out in a 3 dimensional plane? It's interesting how the pattern forms. 2d doesn't do it justice.

[@NimishP]

Here is the link. kzbin.info/www/bejne/qGKbeJxuobienK8 I like 2D version of Fourier series as well.

[@darioinfini]

@@NimishP This must be how they teach engineering now -- with these visual aids. Back when I learned it in the 80's, you were stuck reading equations, explanations, and pretty much accepting on faith that it kind of made sense.

[@sohailahoj755]

@@darioinfini sadly they still teach us like this.. at least for me

[@darioinfini]

@@sohailahoj755 thankfully you CAN see if there are things like this on KZbin that can illuminate a little better. I got virtually nothing out of my notoriously difficult and required statistics class despite getting an A in the course.

[@policedog4030]

@@NimishP Worth watching! Thanks for posting the link.

[@danebeck7900]

Superposition of rotating vectors in the complex plane for each frequency component... Love it! The directivity pattern was pretty sweet too. I work at a company that makes ultrasound scanners and a few years ago I tried writing a Matlab simulation of the directivity of an ultrasound aperture based on the aperture shape and the spectrum measured at the center of the beam. Basically used the same principle illustrated here for directivity. The angles of maximum and minimum intensity came out right but the amplitudes of the side-lobes were off. Never quite figured out where I miscalculated. Very cool!

[@SpeedLuffy]

well loving the concept of fourier series and this awesome music

[@moiquiregardevideo]

Nice choice of color, nice animation. Deserve more views.

[@DJcoasttt]

Very nice, would it be possible to get a version with the corresponding sound wave played? Just to demonstrate the harmonic series with audio.

[@karlbjorn1831]

I keep coming back to this it’s so lovely

[@kristhetimetraveller3120]

This makes so much more sense to me now. Thanks!!

[@michaelklein8974]

I would like to see one that produces square and triangle waves as they are used in synthesisers.

[@unecol]

Perfect! You are a genius! A picture is worth a thousand words!

[@elietheprof5678]

One thing I discovered recently: To make a smooth saw wave without big ripples, multiply the amplitude of the highest harmonic by 0.5

[@elietheprof5678]

And same can be done with a square wave.

[@SHIN2024_official]

I like the music.

[@samuellasky7771]

Oh, to be a Fourier series, just vibing in the void, dancing like a moron just to draw a sin wave

[@ryandennis7023]

So at the top either jump forwards onto another kushind pad or slide down that's a mountain ontop of mountans

[@brogcooper25]

I like. You do great work. Keep it up! The world needs more of this!

[@jwingo7257]

It would be amazing if you could take an EKG tracing and then do a Fourier analysis to break it down into the components from the different parts of the heart as it contracts from the atrium to the ventricles.

[@joshualaporte4459]

The wheel weaves

[@BrekMartin]

the wheel, it spins. It turns around. It makes an ancient rumbling sound.

[@anandarunakumar6819]

Beautiful background music

[@igxniisan6996]

1:00, that thing on the right side looked like something else..

[@SHIN2024_official]

The music starts 18 seconds after the first millisecond (msec).

[@eduardolezano1020]

Great job.

[@oldcowbb]

We will never reach the truth with that gibbs phenomenon

[@hqppyfeet7513]

Getting recommended random simulation videos. This is oddly entertaining

[@ashleypanduro3021]

I love this .

[@j.kendeblanck764]

Great Graphics

[@disectormusic]

Absolute love

[@supriyakurlekar4001]

Great Sir🙏🙏🙏🙏👌👌👌👍👍👍

[@michalvalko248]

Would be great with sound of actual saw wave instead of music

[@Anikin3-]

Look up how to make a saw wave by adding sine waves and then add the sine waves up somewhere you can hear them

[@ve2zzz]

If you pay attention to the cosine, you can see a narrow pulse train.

[@altpraize6708]

How is a triangle waveform made,?

[@SteveAcomb]

this video would be infinitely cooler if you played the tone generated by the signal with each successive iteration

[@gamideoecdysis2872]

What is the song ?

[@abyss2200]

How did animation is made, I'm feeling so excited

[@BrekMartin]

Hi, this is done with Quartz 2D library in iOS Simulator. Basically an iPad App running on a Mac so it can be screen captured.

[@MrImmi34]

what program you used for the animation!

[@BrekMartin]

HI, this was in XCode iOS simulator.

[@MrImmi34]

@@BrekMartinis it possible for you to share the code?

[@MohammadAlshahrani]

Amazing..

[@ブタおにぎり]

この波形の音色がBGMで聞けたら面白さが倍増するかもしれない

[@martinwall8006]

Graphic element is excellent and intuitive. I'm rather new with math. Just starting over. Music was my life. (still is) but math is now my new love! I appreciate the power of Fourier transforms and marvel at the applications of it. But it still feels to me like one of those 'leaves' of science that leaves one wanting it finished? That is to say does a Fourier ever complete? okay be patient with me. I'll be writing some bizarro cool music toward this stuff real soon! I LOVE MATH AND PHYSICS!!! Weeee. (KZbinrs are turning me on like crazy! Mathologer, 3Blue1Brown etc). I can do this! I can do this!!! Watch me mummy!!!!!!!

[@rif6876]

This is very nice! Each circle represents another term in the series, right? That's why the circles get smaller? I'd like to see the term explicitly, maybe on the bottom of the video.

[@mathreyes]

But this is a particular case of all circles are rounding the dame direction, but I have an geogebra applet that translates it to alternated directions.

[@impossiblephysix2633]

What you animated with

[@BrekMartin]

Impossible Physix Hi, this was Quartz 2D library in iPhone Simulator.

[@ericpham8205]

simplest computer is composing of 10 oscilator controlling timer and i/o

[@XevianLight]

Song?

[@BrekMartin]

That’s by Ms Mad Lemon (a retro KZbinr). Utopia it’s called.

[@Baku_man]

circle move is round

[@LordMalleus]

Can you please do the same for a triangular wave?

[@BrekMartin]

If you’d asked at the time maybe :D

[@jsflood]

Nice!

[@SHIN2024_official]

What? Saw wave?

[@timhofstetter5654]

Somebody isn't doing much of a job of clarifying their point...

[@lennykoss8777]

💗💗💗💗

[@Kevin-jc1fx]

I love mathematics 😍

[@ocayaro]

Strictly speaking incorrect because it ignores the discontinuities called the Gibbs phenomenon.

[@nou4898]

i was just about to give a like but i noticed it already had *666* likes and 6 dislikes lol

[@doejames3679]

Solar system#

[@billwhoever2830]

we call a mini spinning line a baby spinning line and the line right before it (the line that holds the baby line) is called a mama line every baby line ever: You spin me right 'round, mama right 'round

[@square_i7380]

benis