title: Fractional discrete Fourier transforms.
abstract: Direct calculation of fractional Fourier transforms from the expressions derived for their optical implementation is laborious. An extension of the discrete Fourier transform would have only O(N(2)) computational complexity. We define such a system, offer a general way to compute the fractional discrete Fourier transform matrix, and numerically validate the algorithm.
authors.forename: Z T
authors.initials: ZT
authors.lastname: Deng
authors.forename: H J
authors.initials: HJ
authors.lastname: Caulfield
authors.forename: M
authors.initials: M
authors.lastname: Schamschula