An animated introduction to the Fourier Transform [video]
He touches on it - but I’d love to see an intuitive explanation of why the response of each frequency to the input function is linearly independent. i.e the fact that Fourier transform of the sum is equal to the sum of the Fourier transforms. This is “why it works” - it’s what makes the frequency space an orthonormal basis - but it’s never been intuitively obvious to
me. Otherwise, there would be more than one way of decomposing a function into a superposition. e.g. what would be useful is to give an example of a set of functions which are not linearly independent.