(Almost-)linear models do linear things, it seems, and the Fourier transform is the quintessential linear thing.
It is also an extremely neat piece of the real world, but I’m hesitant to guess your background and offer an explanation because your phrasing makes me suspect an engineering one. With concepts usually being the first to be culled in a course targeted at engineers, there could be quite a bit of concept debt to pay off before I could really offer something I could honestly call an explanation.
Have you tried the 3Blue1Brown video on the topic[1]? It does not AFAIR offer any answers as to why the Fourier transform should exist or be useful, but it does show very well what it does in the immediate sense.
Thanks for your reply. I think I'm going to have to start reading up on physics/differential equations. My linalg is ok but quite a bit of my computing background has been "here, this is how you calculate it" instead of concepts. I really feel theres something about Fourier that seems pretty important.
It is also an extremely neat piece of the real world, but I’m hesitant to guess your background and offer an explanation because your phrasing makes me suspect an engineering one. With concepts usually being the first to be culled in a course targeted at engineers, there could be quite a bit of concept debt to pay off before I could really offer something I could honestly call an explanation.
Have you tried the 3Blue1Brown video on the topic[1]? It does not AFAIR offer any answers as to why the Fourier transform should exist or be useful, but it does show very well what it does in the immediate sense.
[1] https://www.youtube.com/watch?v=spUNpyF58BY