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 [-pi, pi]. 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/epsilon)) arithmetic operations, where epsilon is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by several numerical examples.