Fast Fourier Transforms for Nonequispaced Data

A group of algorithms is presented generalizing the fast Fourier transform to the case of nonin-teger frequencies and nonequispaced nodes on the interval [-r, r]. The schemes of this paper are based on a combination of certain analytical considerations with the classical fast Fourier transform and generalize both the forward and backward FFTs. Each of the algorithms requires O(N log N + N-log(I/e)) arithmetic operations, where e is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by several numerical examples.