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 basis, 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.
2026-03-27 18:07:46.1774634866
Fast Fourier Transform for non-trigoniometric bases
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