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KIMN'S DESIGNER OUTLET was updated.
10 months ago
KIMN'S DESIGNER OUTLET was updated.
1 year ago
KIMN'S DESIGNER OUTLET was updated.
2 years ago
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https://kimn.neocities.org/circle-wave.html I've read your circle-wave post. First of all, you can represent that graph with trigonometric functions, because you can parametrize the unit circle as (cos(t),sin(t)) for the angle t. So it's already a kind of Fourier series. It's just sines and cosines. By the way, you can use Fourier series to represent almost any periodic functions.
KIMN'S DESIGNER OUTLET was updated.
2 years ago
"Almost any" means anything except some crazy things. At least if the graph is not "discontinuous at infinitely many points in a period", you can use Fourier series without worry. It's because periodic functions make a function space, and sines, cosines make a coordinate system for the space. It's like (x,y) = x(1,0) + y(0,1). Instead of (1,0) and (0,1), you just use sines and cosines.
You should use infinitely many sines and cosines because obviously the dimensions of those functional spaces are infinite. But you can approximate with sufficiently many sines and cosines anyway.