Fourier transform

is there a way to understand this visually and intuitively?

I think I understand the math but when it all comes together it's still magic

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youtube.com/watch?v=r18Gi8lSkfM
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It's magic, man.

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

It's a change of basis

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.

How about this
youtu.be/FjmwwDHT98c

I think this guy overdid it

he neglects the math behind it too much

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

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

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

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

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

This picture shows what happens when you add functions.

desmos.com/calculator/ywlqlixjd3

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

Also study linear algebra and get to eigenvectors ASAP.

This is pretty amazeballs. Thanks user

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

I never even tried to understand the math at all though

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

OP here

I love you user, thanks.

That's Fourier series, not transform

Transform is continuous in the frequency domain

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

...

youtube.com/watch?v=r18Gi8lSkfM

...

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

Thanks mate