Mental Models 4 Life

There’s been a lot written about Fourier Transforms over the years. From a physics perspective, I would recommend the Harmonics chapter in the Feynman Lectures on Physics. I also found Elan Ness-Cohn’s visual explanation of Fourier Transforms really satisfying. In the notes linked below, I have tried to give, in 5 short pages, the intuition behind the algebraic aspects of Fourier Transforms, building on Terence Tao’s article in the Princeton Companion to Mathematics. I hope the reader will get a better appreciation of the beauty of FT by combining these different perspectives.