>>12005785gotchya. personally, i found fourier transforms to be the point where you should stop bothering to do this kind of thinking. i watched a Stanford lecture series on fourier series/transforms not too long ago, and what the professor said after explaining orthonormal vectors (long before getting to transforms) was
>You can't visualize this, so don't worry about it! There's no point. It's reasoning by analogy. The fact is, you establish these formulas, establish they're orthogonal, and then you apply your intuition for orthogonal vectors, where you can visualize it to situations where you can't visualize it. That's the power of this line of reasoning, to apply your intuition to places where it should have no business applying.Like the point is that you have a rectangle function, you know how to do a fourier transform. and you do it, and you find that it has the sinc function as a spectrum. it's a waste of your life trying to intuit everything at this point in math
