Fast Fourier Transforms for Nonequispaced Data

A group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval [ - π ,π ]. 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 (1/ε )) arithmetic operations, where ε is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by several numerical examples.