>the brightness of the circle relates to the energy in the signal

What does this “energy” mechanically correspond to in the complex unit circle and how do these mechanics appear in the time-domain?

The ideal low pass filter’s mathematical application - of the frequency domain effects on natural signals - astonishes me and I can’t quite fathom the transformation; ie is the frequency space physical or a purely mathematical abstraction?

Ultimately: is the complex exponential function a natural algorithm?