Sine Wave to Square Wave using Fourier Series
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Uploader Comments (Russoft)
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the 60 hz scared me lol
2 years ago 19
All Comments (84)
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ooooo, oooo, oooo... dum-dum-dum-dum-dum-dum... DAA-DAAA!!! What's the name of the song?
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@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.
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SHIT FUCK OW.
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@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.
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MY EARS!!!!! AAAAAAAAAAH!!!!!! IT BURNS!!!!!
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@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.
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@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.
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@andrewdalecramer Referencing YouTube? What kind of idiot would do that
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@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.
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fucking fourier series. hated that shit.
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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,.
Basmund 3 years ago 4
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.
Russoft 3 years ago 4
when n approaches infinity, the wave become a square wave?
en14vn 3 years ago
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.
Russoft 3 years ago