zlacker

>>qqqqqu+(OP)
Fourier Transforms. I'd wish I had a intuitive understanding of how they work. Until then I'm stuck with just believing that the magic works out.

>>rambol+mj
The intuition of Fourier Transforms is that any continuous, repeating waveform can be recreated by the addition of harmonics of a sine waveform eg a square wave, IIRC, is the addition of the odd harmonics.

The cool thing about this insight is that the converse is true. You can disaggregate any waveform into its additive harmonics. This means you can jam multiple signals into a single channel (eg a fibre optic cable) and then apply a fourier transform at the other end to "untangle" them.