I don't see what the article is trying to get to. It certainly doesn't answer its own question in the end. Fourier transform is not the same thing as the DFT t

I don't see what the article is trying to get to. It certainly doesn't answer its own question in the end. Fourier transform is not the same thing as the DFT to begin with. Thinking of the Fourier transform as just the decomposition of signals into sine waves may not be the right way of looking at it either. A very useful feature of Fourier transform (and Laplace transform, more generally) is to convert ordinary (and some partial) differential equations to polynomials, which turns solution of differential equations to polynomial algebra. This was also the original goal of Mr. Fourier for solving the heat equation. Are there other transformations that can do that?