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 … More Algebraic Intuitions behind Fourier Transforms