cross-posted from: https://lemmy.world/post/52070794

Check out the university level maths education on my website: https://www.cmmath.org/

0:00 Intro
2:52 Orthogonality
3:50 Eigenfunction Expansion
8:13 Legendre Series
17:11 Fourier Series
28:18 The Basel Problem

You can literally describe anything using Fourier functions. That should tell you something about the universe.

i don't think i've ever had a use for this piece of knowledge -- can you give some examples?

Fourier transform can be used to describe a single square pulse.. That means in n dimensions, Fourier transform can be used to describe any geometry or pattern. That means that any physical relationship can be described by a combination of sines and cosines. Its power is unbelievable.

yeah, that's what i've been told in school, but i still have yet to see a use for it since then besides what's already been engineered into electronics.

Hard to give an example that would be relevant to your particular activities, but violin makers sometimes use it in a practical way.

When you make a wooden soundboard you can
visualize its deformation eigenfunctions (or rather its zeros) and proper frequencies using a speaker and sand:

https://www.youtube.com/watch?v=_l2Uh5EVxB8

And they use it to "tune" the soundboard somewhat as far as I understand it ?

Also, for the strict "anything described in Fourier" proposition, you can draw homer Simpson with epicycles with it:
https://www.youtube.com/watch?v=slfS7j_7L6s

So I guess all the 1400's astronomy was using it somewhat

It should rather tell you something about Fourier analysis

What field are you in?

computer systems administrator and former software engineer.

Time-frequency analysis and autoencoder approach for network traffic anomaly detection

Enhanced Detection of Malicious Network Traffic Using Frequency-Domain Analysis

Mining Graph-Fourier Transform Time Series for Anomaly Detection of Internet Traffic at Core and Metro Networks