An Intuitive Explanation of Fourier Theory

From the first section, basic principles:

"any signal" huh? "spatial frequency" 2x huh? "a "DC term" corresponding to zero frequency" #seriously

This is intuitive only if you already know this stuff, which I happen to, but I have also tried to explain this to undergrads taking history and english. Terms like these are not intuitive at all.

The curse of knowledge[1], also known as: Teaching is a skill worthy of great respect.

[1] https://en.wikipedia.org/wiki/Curse_of_knowledge

I take intuitive to mean non-rigorous not introductory.

Here's a tool that let's you try the transform interactively: http://www.ejectamenta.com/Imaging-Experiments/fourierimagef...

Curious... If the Fourier transform can be 'calculated' by photons passing through an optical lens, has anyone ever produced a component that could capture the computation numerically? I.e., some sort of capsule/chip with:

* A digital-to-analog converter with pixel array on one end * A lens in the center * A sensor array with an analog-to-digital converter on the other end