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Why are Fourier transforms so ubiquitous and useful explanations of phenomena?

Anonymous Fri 05 Feb 12:28:45 2021 No.12670004 View Reply Original Report

Quoted By: >>12670006 >>12670027 >>12670038 >>12670058 >>12670384 >>12670660

Anonymous

Anonymous Fri 05 Feb 2021 12:30:17 No.12670006 Report

Quoted By:

>>12670004
Useful in* explanations of a wide variety of phenomena

Anonymous

Anonymous Fri 05 Feb 2021 12:37:23 No.12670027 Report

Quoted By: >>12670072

>>12670004
well... it's frequency analysis
you learn a lot by seeing how often something occurs

Multimorph

Multimorph Fri 05 Feb 2021 12:41:29 No.12670038 Report

Quoted By:

>>12670004
For physics, all collisions cause vibrations. Fundamental particles are pure waves. Plus fourier applies to many functions, and most things are functions. Even your table can be drawn with 3d fourier transform, its a bunch of coordinates in space

Anonymous

Anonymous Fri 05 Feb 2021 12:49:16 No.12670058 Report

Quoted By:

>>12670004
Because when you shift a complex exponential function, that is equivalent to multiplying it with a number, i.e. complex exponentials are the eigenfunctions of the shift operator. This also means that a lot of stuff in the physical world (e.g simulating heat diffusion) is literally as simple as multiplication in Fourier domain.

It's all because of this fundamental fact.

Anonymous

Anonymous Fri 05 Feb 2021 12:57:21 No.12670072 Report

Quoted By: >>12670089

>>12670027
t. Retard

Multimorph

Multimorph Fri 05 Feb 2021 13:12:51 No.12670089 Report

Quoted By:

>>12670072
Terveisin retard

Anonymous

Anonymous Fri 05 Feb 2021 15:50:15 No.12670384 Report

Quoted By: >>12670615

>>12670004
It's a complete orthonormal basis, hence you can always expand any function as an infinite series in it. There is nothing unique about using sines and cosines, it was just was the earliest and simplest transformations done. You can use any basis so long as it creates a complete orthonormal basis. Bessel functions work as well, and are used all the time in PDE.

Anonymous

Anonymous Fri 05 Feb 2021 16:04:55 No.12670416 Report

Quoted By:

Because nature is complex and that formula simplifies it the best

Anonymous

Anonymous Fri 05 Feb 2021 17:23:02 No.12670615 Report

Quoted By:

>>12670384
Well said. Youre leaving out alot though so i wouldnt take what youre saying as anything more than intuition.

Anonymous

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Anonymous Fri 05 Feb 2021 17:33:51 No.12670660 Report

Quoted By:

>>12670004
Cuz Waves n'shiet (Explanation in Ebonics)

Technical Explanation: Useful for Anything Periodic.
Any periodic function can be decomposed in a Series of Sines and Cosines through Fourier Analysis.
Periodic phenomena such as Vibrations and Waves are abundant in Physics that why its so useful.

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