The Nineteenth Byte

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11:02 PM

@flawr I had a math question

can one derive the fourier transform by taking the inverse fourier transform which can be derived basically from common sense, and then solving for F()? I couldn't get anywhere with that approach

Dmitry Kudriavtsev

File.read("/usr/share/dict/words").split.map{|i|i.gsub("'s","")}.shuffle[1..5].‌join(" ").capitalize+"."

noɥʇʎPʎzɐɹC

> I think Randall has a time machine and checks Reddit a couple years ahead for the phrase "I don't have a relevant xkcd!" and then comes back and makes it to prevent that timeline from occurring.

feersum

@Maltysen Do you know linear algebra?

noɥʇʎPʎzɐɹC

edition.cnn.com/2016/11/01/us/…

number overflow -> 43 mil jackpot

Maltysen

@feersum yeah

basically

feersum

11:10 PM

So if you do the type with discrete coefficients (that can form only periodic functions), it's relatively straightforward

quartata

@PhiNotPi But it was!

Maltysen

@feersum you mean the fourier series?

feersum

You can show that that sin/cos n pi x forms a basis for the space of periodic functions

@Maltysen Right

Maltysen

that's what I was shown

no linear algebra, just a proof of the series, then take limit period → ∞ gives transform

but since the inverse transform seems so easy, I was wondering if it was possible to use that to prove the transform

feersum

Well for the series, you can show that it's a basis, meaning that to invert it you use the inner product to find the weight of each function

I don't know exactly how to show that for the continuous version.

Maltysen

11:14 PM

@feersum oic what you mean

yeah, that's why I was saying that the inverse is super easy to derive

but I was wondering if i can use the inverse to derive the forward

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Maltysen

but the change of basis idea is pretty cool

feersum

Oh when I said invert I actually meant the "forward" way

Maltysen

@feersum ohhhhh

feersum

Oh it should be n pi x / L where L is the period of the function

Maltysen

11:16 PM

so that's why the forward is just the same as the inverse

(*-1)

oh you meant inverting the change of basis

Nathan Merrill

11:35 PM

@noɥʇʎPʎzɐɹC I keep trying to figure out how they got that number, but it's not just simple integer overflow

mınxomaτ

@El'endiaStarman Ah, whoops. I made a math error in the JS benchmark. It's actually plenty fast, but GPGPU still gives a massive improvement.

TIL calculations that result in NaN really stall JS.

flawr

@Maltysen I don't quite get what you're asking

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Downgoat

@mınxomaτ s/that result in NaN// :P

mınxomaτ

Well, I fixed that

Hence this whole project

Maltysen

11:48 PM

@flawr thanks but @feersum cleared a lot of things up for me, which made me realize that my question was pretty stupid

flawr

Ok=)

All in all it is worth noting that the fourier transform and its inverse are basically the same thing. (in the discrete aswell in as in the continuous case)

(up to some "constants")

Maltysen

@flawr is there an intuitive reason why that is so?

flawr

There was a really nice explanation, let me see if I can find it.

i-programmer.info/programming/theory/…

The idea of wrapping a signal around a circle (with a given frequency/angular velocity) and averaging (=sum or integral) the points to get that share of the signal is a really helpful image.

If you got that, it is easy to see that the inverse basically consists of doing the same again.