What is it good for?

>>8312824
Sheeeeeeeeeeeeeeeeeeeeiiiiiitttt

liek, wehn are we even gunno like use dis calculus shit in da real world anyway, niqqa?

https://en.wikipedia.org/wiki/Convolution#Applications

>>8312824
It's pretty in Laplace space

heat equation

image processing

>>8312824
Lineal systems. Aka everything that is useful.

>>8312824
absolutely everything that involves a signal

from telecommunications, to seismology, to financial analysis... every single filter applied to every signal is (and if it isn't, it is approximated as) a linear one, and applied through convolution

Let's say that [math]f(t)[/math] and [math]g(t)[/math] are simultaneously convolving with the output of [math](f*g)(t)[/math] with some delay [math]Y[/math]

How long does it take for [math]f(t)=g(t)[/math]?

>>8312824
>fgt
>fot frgt
>r
>dr
It's good for insulting people.

linear systems, so just about anything involving signal processing

Absolutely nothing! (Uh-huh)

>>8312824
Good for regularizing functions and create good test-functions.
Also good in probability theory for the law of the sum of densities.

Think about stuff that is delayed by some degree, but still it has an influence on the present situation. Like retarded electric field.

absolutely nothing!

>>8312909
>r

That's tau, you fucking mongoloid.

>>8313576
Or OP himself.

Is it better than triple integrals?

File: Screen Shot 2016-09-01 at 12.06.05 PM.png (14KB, 476x96px) Image search: [Google]

14KB, 476x96px

>>8314597
I dunno, lol

Convolution neural networks use it and machine learning will replace you eventually so I'd say it's used for everything

>>8312824
>>8313595

Say it again, y'all!

>>8315781
Can machine learning create anything new, or does it only approach existing information?

>>8315814
Answer the same question about humans.

Yes machine learning algorithms can create new concepts, but they are based on the ones it was trained on. Much like our selves. Only difference is ML cam process higher dimensional data as well as larger sets of data much faster.

>>8315843
Right now, Siri can only answer questions. Eventually, will she be able to say everything I want to say, before I say it?

>>8312824
It's an integral of two functions that can be converted to a product of functions and back by the Fourier transform and its inverse. That's cool. Also statistics. The "sum" of numbers coming from independent events will have a distribution which is the convolution of the two distributions.

>>8315890
Probably not, there will be no incentive for siri to want to call a girlfriend or set up a volleyball club or set an alarm to wake up. She might predict that you will want these things, but the computer itself won't probably develop these desires as they come from biological needs.

Siri may however be able to make a conjecture about some study or dataset that you would never be able to and then prove it.

>>8316534
>A computer wouldn't care about your biological needs
>it WOULD care about abstract mathematics for some reason
Kay you lost me there

>>8312824

>Higher Spin theories
>Topological theories
>Poisson sigma models

A bunch of theoretical physics use this or related ideas.

Hey guys, what happens when I take out the asterisk?

i hate math desu
why is math allowed to post on a SCIENCE board????

>>8316559
What's the best way to improve existing algorithms? Better mathematical framework.

>>8312824
ABSOLOOLEY NUTIN'

Telecommunications engineer here.
It's my bread and butter.

>>8312824
>Do Electrical and computer engineering
>Use Laplace, Fourier or Z-transforms in literally everything
>Should rename ECE to Integral Transforms: The Degree

>>8316559
Also I'm not saying it wouldn't care about YOU'RE biological needs, it just won't have any of those needs itself. Also there is a fundimental difference between our motivations and an AI's that is entirely based in biology, even if the way they learn is very similar.

>>8312826
>overt internet racism

why and how does one care enough to do this

>>8316896
i'm black and fuck off pussy, that's what anonymity brings

>>8312824
It's the natural generalization of abstract polynomial multiplication:

[eqn]p * q =\sum_{k}\left (\sum_{i+j = k}p_{i}q_{k} \right )x^{k}[/eqn]

to the continuum.

>>8317723
This is the right expression,

[eqn]p * q =\sum_{k}\left (\sum_{i+j = k}p_{i}q_{j} \right )x^{k}[/eqn]

>>8313287
underrated post

>>8312872
How?

>>8312824
I use convolution with a gaussian, combined with a median filter as my first attempt at smoothing noisy data. Between the width of the gaussian, and the width of the median filter I have good results in most applications involving accelerometers and and tachometers.

>>8317941
... That's not the same type of convolution though. Matrix convolution isn't integral convolution of functions, right?

>>8317947
make the step size small enough and they converge exactly

>>8317949
Oh shit. I've realized my mistake, sorry

>>8317947
also replacing a polynomial with a matrix using a finite step size is the simplest way to solve just about any differential or partial differential equation using finite difference approximation. This is how convolutions are used in control systems as well, all input signals are discretized and operated on in parallel in fpga or asic processors.

>>8312824
my entire thesis

>>8317959
That makes a lot of sense, thanks

>>8316896
>racism
It's an accurate stereotype for a large subset of African Americans. Nothing racist about that. There are, of course, many black people who aren't retarded, as well.

>>8317512
>that's what anonymity brings
I openly mock braindeads in real life.

>>8313287
I came here just to post this. Nice.