While of course one can use whatever orthonormal basis one likes, and so in particular one can use the one shown in the article, uh, I’m not sure what stateme

While of course one can use whatever orthonormal basis one likes, and so in particular one can use the one shown in the article, uh, I’m not sure what statement that others might believe, the article is contradicting? The Fourier transform has some nice properties that other bases don’t. One way to view the Fourier transform, is as decomposing “the space of functions on [some domain], regarded as a representation of [the group of translations in that domain]”, into one-dimensional sub-representations. (Or, if you want to stay over the real numbers instead of complex numbers, then two dimensional representations) I don’t know that there’s a nice analogy of this for the basis described in the article. Maybe there is? Like, maybe if one uses some group with 2^n elements other that Z/((2^n)Z) , maybe (Z/(2Z))^n, then maybe the basis you would get would be like the one shown? Idk. But I don’t see this as showing frequency space as less real.