I was watching a video while learning the intuition behind the Fourier transform, the link to the video is: https://www.youtube.com/watch?v=spUNpyF58BY&t=150s
My question is, at 4:47. Why does the Fourier graph attain a 'peak' when the winding frequency matches the frequency of the signal?
How do we formalize this question mathematically? Is this statement a result of some theorem(s), what are their names?