The Fourier Transform, explained in one sentence

If, like me, you struggled to understand the Fourier Transformation when you first learned about it, this succinct one-sentence colour-coded explanation from Stuart Riffle probably comes several years too late: Stuart provides a more detailed explanation here. This is the formula for the Discrete Fourier Transform, which converts sampled signals (like a digital sound recording) into the frequency domain (what tones are represented in the sound, and at what energies?). It's the mathematical engine behind a lot of the technology you use today, including mp3 files, file compression, and even how your old AM radio stays in tune. The daunting...