[woopsn]

I agree overall. But a note - every orthonormal basis partitions the frequency spectrum. It doesn't go away, if you are using e.g. polynomials then you're building functions up out of their frequency components too. The Fourier basis has every element correspond to a specific frequency, which is special in some sense. I would say rather.. they are each designed for a purpose. A basis change can rearrange the spectrum in such a way that analysis of it is complicated. Then you're analyzing something else (eg smoothness). Most functions of interest do have distinctive spectra, even if the Fourier basis doesn't answer all the questions.