7
$\begingroup$

The fast Fourier transform allows decomposition into a sin/cos basis in $N \log(N)$ complexity. Can one generalize the algorithm (or the ideas used) to other bases, e.g. orthogonal polynomial bases such as Hermite, Legendre, Chebyshev,...? I have a special interest in Zernike polynomials as well. If so, how? If not, what is special about the sin/cos that separates it from the other cases?

Also asked previously on: https://math.stackexchange.com/questions/647613/fast-fourier-transform-for-non-trigoniometric-bases/1730645#1730645 not having quite a satisfying answer yet.

Also, in a related question here on MO (here), I see pointing to this document on why the FFT would be fast. How could I use this principle on general orthogonal bases?

$\endgroup$
2
$\begingroup$

Related questions have been considered in some depth by Dan Rockmore and collaborators. For more, check out Rockmore's web page.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.