Circle waves—PLEASE HELP ME

Hi, just a short post about something that's been absolutely killing me.
If you know anything about music synthesizers, then you'll know that they can produce different wave forms like

Sine Waves
Square Waves
Sawtooth Waves
Triangle Waves

And you make these waves by layering a bunch of sine waves on top of one another until you get the desired result—with something called a fourier transform which I'm not nearly smart enough to understand how to do.
Anyway, the point of the article is that surely we can do this for a wave that's made out of circles—one that looks a bit like this:

Instead of intersecting the x axis at a 45 degree angle, it would intersect at a 90 degree one. Surely it would be possible to make her using the fourier transform? If you think you could have a stab at this, I've been itching to hear what it sounds like for almost a year now.

That being said, I wouldn't expect it to sound particularly ethereal or special, as they all seem to be on a fuzziness spectrum with the pure sine being at perfect smoothness, and the square wave being at perfect fuzziness. In other words I'd just expect it to sound like a slightly buzzier square wave. But if you can, do it just for the sake of science and make sure to email me about it!