Sine Wave to Square Wave using Fourier Series

[CognitiveNetwork]

ooooo, oooo, oooo... dum-dum-dum-dum-dum-dum... DAA-DAAA!!! What's the name of the song?

[SlapPopStacy]

SHIT FUCK OW.

[camelCaseFTW]

MY EARS!!!!! AAAAAAAAAAH!!!!!! IT BURNS!!!!!

[muddwell]

fucking fourier series. hated that shit.

[xolapower]

Anyone familiar with a square wave knows that those sounds were not correct. A pure square wave is a bit like a clarinet, much prettier than what you heard at the end.

(And yes, a perfect square wave is not possible, but easy to get very, very close to perfection)

[zyxomma1]

That was nothing like a square wave.

[darkshadowvamp]

Sounds like a ground problem to me..

[zomgrandomtext]

WHY DO I KEEP LISTENING TO THIS WHEN IT HURTS SO BADLY

[rosskay]

@zomgrandomtext :) I have a bit of a thing for square waves too. something about it feels so addictive and attractive.

[TractorTheBassist]

WoW

[elARTEdelPOOP]

There is another way to replicate square wave using just one sine wave.

This can esily be done by adjusting the volume of the sine wave to a certain point that the scale graph.

In other words, just volume up your sine wave in order to do a square wave.

[Jamesia]

@elARTEdelPOOP umm.... no.

[ACarbonBasedLifeForm]

wow, my teeth are cleaner having watched this....thanks!

[TheAlveral]

can we construct a simple circuit that converts sin to square wave??

[zep4life]

Note how similar the square wave at the end sounds to 60hz mains hum. You can hear the harmonics. Reminds me of when you unplug an electric guitar and drop the cable! cool video

[wwwpat]

good work! thank you!

but you should really set a warning before playing the tones. with headphones this demonstration can really hurt.

[SmithvilleFlats]

Any music geeks know what intervals those were?

[Joshplaysinstruments]

from n=0 to n=1 it's a P5

from n=1 to n=2 it's a M6

from n=2 to n=3 it's a tritone

from n=3 to n=4 is a M3

[Joshplaysinstruments]

n=4 to n=5 is a m3

n=5 to n=6 is a M2

n=6 to n=7 is a m3

7 to 8 M2

8 to 9 is another M2

hope that helps.

[boobtuber06]

what are some moder applications of square waves/sawtooth waves?

[triden55]

@boobtuber06 electronics are full of them. Mostly every digital logic circuit is pulsed with square waves. Your computer "speaks" in square waves (on or off) at its lowest level.

[falohao]

how about vice-versa???

[smpaudio]

What happens at :58? Is that a different wave being compared to the additive one?

[ScalarPhotonZ]

It seems like the first frequency has been transposed a number of octaves up, in which case, I would not expect the sound produced to resemble a square wave. Am I right?

[mikeswbr]

are they done at the right volumes? that's a really cool demonstration.

[FreezingSun14]

the 60 hz scared me lol

[Activethrasher00]

this is what you get when you push your power amps too hard?

[fingerboy18]

Not quite.  That is called clipping. It's when the amplifier's gain stage is driven too hard and peaks of the waves flatten out. Transistors and vacuum tubes react differently. Transistors tend to create sharp clipping much like a square wave. Tubes have smoother clipping characteristics.

[fukdyamum]

anything above 0db is effecting the waveform, you keep clipping the roundness of the sine wave and it becomes square.

I think you mean pre amp btw

[SaeBap]

@fukdyamum so its the overdrive / distortion you get in your Marshall Stack..

[thefaketahare]

exactly why tube amplifiers are considered de rigueur for serious guitar players

[Deluxeta]

How do you call that sound effect that sound kind of like a ring modulator when a sound wave is "squarified"?

[dudemanbearpig]

I'm awfully disappointed. I saw a video with "square wave" in the title and expected ear rape.

[djwilliamt]

damn gibs phenomenon

[BoogsterSU]

LOL I remember, Lombard Street is shaped like a sine wave!! :-D (sorry I'm still high school freshman, but can't wait to learn about this lesson when I am older!! :-D)

[beenn15]

why wait. get a book from the library and start learning this stuff. Even if you don't understand everything at least you'll be familiar with the concept

[SPS148669]

So this is how they make music in oldschool 8 bit Videogames like the Nintendo NES I believe.

[joewhittles]

depends. I dont think theyd make the square wave by mashing a bunch of sine waves in at the same time, i think you only got 4 audio channels or something in a nes! don't know exactly how they did it, but i'd think it would work like some kind of duty cycle where the on/off time would depend on the frequency.

[fingerboy18]

More like modular analog synthesizers from 60's and 70's rock like Pink Floyd. A ton of analog voicing.

[wackid89]

That's cool. Good to know all those pages of working I do in maths can actually be used for something!

[eazylee369]

Funny, I was just messing with this function on my laptop using mathcad. No sound effects though!

[cwldoc]

Very interesting! Many years ago I studied Fourier series on paper, but I never actually got to hear the successive approximations.

[Basmund]

Theres no such thing as a "perfect" squarewave. it simply just cant be heard! not in this dimension atleast. you cant have a loudspeakermembrane move from one position to the other in 0 seconds. It's against the law of physics,.

[Russoft]

I take it english isn't your first language? By putting perfect in quotes: "perfect" I merely meant "as close to perfect as my computer can play". Obviously a perfect square wave is entirely theoretical.

[wackid89]

You can keep going closer and closer to a square wave but then eventually Heisenberg's uncertainty principle comes and screws you over lol

[princeofexcess]

@Russoft English isnt my first language but at least I know a fallacy when i see one. Other then that you are right on the quotes

[Aqlor]

@Russoft it is perfect. you just dont have everything you need to play it. on the computer it will jump change from one state to the other. YOUR speakers aren't just good enough

[Basmund]

@Russoft Then we agree. I am sorry about the attack there :) I was a bit too fast, and I guess I just wanted to yell out that the perfect square can't be produced/experienced in physical form, since I had just discovered that... 2 years ago.

[rosskay]

@Basmund I disagree. I had an acoustics professor bring in recordings of square waves and played supposed frequencies that should have been 'theoretically' inaudible, including dissonant and consonant harmonics. I was able to pick up on some of them, and could even point out that a number of them were actually "flat." (the recordings claimed to all have the same perceived fundemental frequency) He did not tell the students this, until I complained about it out loud... and said i was correct.

[Basmund]

@rosskay What you heard could not have been a perfect square wave, but only the speakers trying their best to recreate one. As Russoft also put it; The perfect square is entirely theoretical.

[rosskay]

@Basmund I understand that speakers can't move to actually form a true square wave, but it is in fact true that people can experience it. Mind you, I'm a wierdo that can perceive see and feel things the avg person can't, so....

[Basmund]

@rosskay If the speakers can't create it, how can you then perceive it? Please explain what you experience.

[rosskay]

@Basmund I posted on your channel, comment was too long

[YouFailEpic]

@Basmund doesn't the law of physics leave room for the existance of worm holes? and if so, wouldn't putting a loudspeakermembrane in a worm hole the length of its xmax enable it to move from one position to the other in 0 seconds? yes, it would.

schooled.

[mherzl]

This is amazing. Thank you.

[schizoflux]

n=10 or what have we, a sine becomes a square? Due to the overlapping harmonics right? What about a sawtooth?

[wackid89]

Saw tooth is the same but with like n^2 in and shit. Get's fucked up when you have having 'curved' sawtooths

[Amishman35]

Think you haven't heard a square wave in a while? Listen to your NES, Gameboy Color, or Atari 2600. And 60 hertz is the mains frequency in the USA. If you use a shortwave radio, you can pick up the 100,000th harmonic on it if there's a cable modem nearby and you tune to 6 Mhz.

[en14vn]

when n approaches infinity, the wave become a square wave?

[Russoft]

not really, but almost. There will be odd spikes at the top and bottom of the vertical sections. You can see the pattern as n increases.

[hboy007]

(The spikes are called Gibbs Phenomenon)

[amschaefer257]

@Russoft yeah, see gibbs phenomenon

[Jamesia]

@Russoft @en14vn just to add that if n does reach infinity then it will be a perfect sine wave.

[XFi6]

@Russoft As n approaches infinity, the artifacts become smaller width. Once at infinity, you could say the artifacts are nonexistent for being so thin.

[andrewdalecramer]

@Russoft In the limit as n approaches infinity the spikes disappear. The fourier series will match the square function at all places except for the jump discontinuities where it will take the value of the average of the right and left hand limits, i.e. the half way point of the jump.

3 yr old post I know but just in case someone references it.

[Roksonixx]

@andrewdalecramer Referencing YouTube? What kind of idiot would do that

[andrewdalecramer]

@Roksonixx Haha, you're right on that one. If they're truly referencing youtube then they deserve to get it wrong, but it's still good to have correct information where possible.

[abrelosojo]

@Russoft the fourier series approximation converges pointwise to a square wave, but it doesnt converge uniformly. ie with a large enough n you can make any point as close as you like to 1/-1, but no n, however large, will guarantee all points are as close or closer.

[polvoazul]

@abrelosojo NOoooo. the series does not coverge pointwise!! Just take a look on whats happening near the point where the squarewave goes to -1.

The series does converge, however its a diferent kind of convergence: L2-norm convergence

In short, it means that the area between the functions (series & squarewave) is as small as you want. And please, do research before arguing, i know what i am talking about.

[daboos86]

oh...now i understand :X

thanks a lot. I'm studying this for my sound tech exam this gives me a good understanding of square waves and harmonics :D

[beranharp]

this video is awesome, especially when heard through headphones, just make sure the volume isn't up too loud. But hey, if it is, maybe it will do something good to your head. One suggestion I would make for improvement is to go from sine to square wave and then go backwards to sine wave again. This truly shows the intellectual potential of Youtube though. Thanks!

[valveman12]

WARNING!

Don't watch this video with headphones on.

OUCH!

[Russoft]

Sorry man, guess I shoulda put a warning about that :P

[pilopiloCH]

i've just done that

OUCH too

thanks for the suggest lol

[Russoft]

Given that it satisfies several conditions, such as being periodic. Even then you do get some error (if you notice higher n have irregularities at the drop and rise of the wave).

[selimhuseyin]

just a perfect presentation:)

[RedBull3220]

try 10000

[sourenaair]

No the real point of fourer series is" the representation of any periodic singal in to a combination of sin and cos functions. therefore, we are transfering the time domian in to frequency domian representation.

[Russoft]

I hadn't learned that 3 months ago. Now I know that :P

[adb4]

UofA EE represent. :D

[Russoft]

it...actually does, although that isn't the point of it. The point of it is to be able to mathematically represent any shape of wave with functions that can be differentiated, integrated, etc. And it's just plain cool :P

[kris2pe]

n=0 causes the audio to sound funny! Wow for someone who is home-schooled you really are smart!

[Russoft]

Being home-schooled says nothing as to how smart you are. There are lazy home-schooled kids, and motivated ones. I was motivated, and that is how I made it to university. Anyway, I wouldn't say I am smart, but I AM curious and like to learn.

[kris2pe]

But being home schooled has its limitations. Like... where do you get books? Who's going to teach you these things? Who's going to monitor you or grade you?

Sorry we don't have home school programs in my country!

[Amishman35]

I will always keep my mind closed that home-schooled children are the bratty near-dumb ones.

[kris2pe]

Hmm interesting! Wat's the point of this thing anyways? It does some how disrupt noises or sound quality of audios if you play this video w/ another audio or video!

[gimplar]

The point is to represent any integratable function as a finite summation of complex terms. The coefficients of these complex terms describe the freq spectrum of your original function and phase data is encoded into the complex exponential.