Your sentence describes what the Fourier transform is, whereas the sentence in the article tries to describe how the Fourier transform does it. What the articl

Your sentence describes what the Fourier transform is, whereas the sentence in the article tries to describe how the Fourier transform does it. What the article does is translate the mathematical notation to a sentence in English, attempting to retain all the information in the mathematical notation. It can be helpful if you are trying to visualize what each component of the mathematical notation is doing, but if you separate the sentence from the equation, it is not very helpful. For example, how would you interpret "spin your signal around a circle"?