[bbtn]

I don't know if this kind of visualizing Fourier transform is helpful to anyone doing/will do work using this idea, but it is not useful to me, and I don't think it is useful to anyone, apart from being somewhat interesting representation, in a way an illusion.

Here is how I see this:

-Sinus (and cosinus etc) is defined using a right triangle, unit length hypotenuse simplifies things, so they are shown on a right triangle inside a unit circle.

-Time dependent sinus function, sin(wt), can be represented using a uniform circular motion and y coordinate of position.

-Fourier says that you can represent (may be almost all) functions using sinus functions with proper frequencies and amplitudes. There is a way to find those coefficients using some mathematics: infinite or finite sums or integrals depending on application.

-Oh well, I have a wonderful idea, great analogy, listen: why not show Fourier transform/series using a circle on circle on circles, uniformly moving (constant speeds) particles and projections of their position to sideways as a function of time.

I don't think understanding its mathematical form is more complicated than understanding what a function is. It is already very simple, too much enforced simplification makes it complicated.

[diger44]

Hi, creator here,

I appreciate your feedback, my eventual goal of this site is to expand to concepts like directly using FFTs with arbitrary waves where your suggestion might be constructive, as yes circles on circles does make it seem more complicated than it is. One of the goals of this specific visualization was to demonstrate how fourier series relate to oscillators and sound, in which case a circle representing a frequency or set of tones added together made more sense.

For reference, I did not personally come up with this particular style of representing Fourier Series, I based it on this: https://commons.wikimedia.org/wiki/File:Fourier_series_squar... which is used on the main Wikipedia page about Fourier Series themselves.