/sci/ - Science & Math

It's magic, man.

The more I use and learn about Fourier transforms the more amazed I am by them

>>8441001
It's a change of basis

>>8441001
I think it's kinda similar to breaking up a number into its prime factors.

You break up a signal in its different frequencies I guess.

>>8441001

How about this
https://youtu.be/FjmwwDHT98c

>>8441104
>>8441104

I think this guy overdid it

he neglects the math behind it too much

>>8441117
Op wanted to understand the concept not the math,
that's what he asked for, nothing more and nothing less

>>8441001
I think what you're implying with the image is a Fourier series. Fourier transforms are easier to visualize if you know some of the basic transforms, rect, delta, sinusoid, etc

>>8441126
The math IS the concept. The rest is computation, human intuition, and graphical software packages.

>>8441159
>Math is the concept
No, not really being able to see relations and putting them into equations is an entirely different skill set.

>>8441167
The math behind the fourier transform is very basic. If you cant relate what it is expressing intuitively with respect to the transformed signal stem might not be for you

>>8441001
This picture shows what happens when you add functions.

https://www.desmos.com/calculator/ywlqlixjd3

Literally all that's going on here, graph it out.

Also study linear algebra and get to eigenvectors ASAP.

>>8441104
This is pretty amazeballs. Thanks anon

>>8441159

I can use an FFT and get useful information out of it easily

I never even tried to understand the math at all though

>>8441001
have you taken any linear algebra?
x and y are linearly independent and thus form a basis for 2-space.
y=cos(x) and y=sin(x) are also linearly independent. Actually, cos(nx) and cos(mx) (and similarly sin(nx) and sin(mx)) are linearly indepenent if n does not equal m.
Thus any function can be represented by some linear combination of cos(nx) and sin(mx).

This means that the infinite dimensional function space (a generalized vector space where each vector is a function) of {cos(nx), sin(mx)} (n,m positive integers), which contains all possible linear combinations of sin and cos, is guaranteed to contain (or be) a basis for your space.

The Fourier transform is the transformation which takes your function, represented in the (x,y) basis and represents it in this new basis, making use of an infinite sum of inner products (you may know one use as the dot product) which takes the function and returns the component of that function in each basis element's direction, and thus the sum over all basis elements gives you the representation of your function in this new basis.

Sorry if I made any mistakes, I cbf to read what I just wrote so...

>"I took the data into Windows"
>"I plotted the data with Windows"
>OSCON: Open-source Convention organized by O'Reilly
Wew

>>8441492

OP here

I love you anon, thanks.

>>8441063
That's Fourier series, not transform

Transform is continuous in the frequency domain

>>8441598
Fuck off with your cynicism, that was a good presentation.

https://www.youtube.com/watch?v=r18Gi8lSkfM

>>8441001

>>8441159

Well then you weren't paying attention because he defined the mathematical formula to calculate it then he showed how that translates to psuedocode then he explained how you can use C to implement it.

So.. you're dumb

>>8441191
Thanks mate