Because it's Friday: Visualizing the Discrete Fourier Transform

A couple of years ago I suggested a way of thinking about how the Discrete Fourier Transform works, based on Stuart Riffle's elegant colour-coding of the equation: (Sadly, Stuart's original post describing the equation has been lost to bitrot, and can't even be found in the Wayback Machine.) My contribution was the following analogy: Imagine an enormous speaker, mounted on a pole, playing a repeating sound. The speaker is so large, you can see the cone move back and forth with the sound. Mark a point on the cone, and now rotate the pole. Trace the point from an above-ground...