Fast Fourier Transforms for Nonequispaced Data Alok Dutt Yale University 1993 Two groups of algorithms are presented generalizing the fast Fourier transform (FFT) to the case of non-integer frequencies and nonequispaced nodes on the interval [-7r, 7r]. These schemes are based on combinations of certain analytical considerations with the classical fast Fourier transform, and generalize both the forward and backward FFTs. The number of arithmetic operations required by each of the algorithms is

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... oportional to N-log N + N-log(I/e), where 6 is the desired precision of computations and N is the number of nodes. Several related algorithms are also presented, each of which utilizes a similar set of techniques from analysis and linear algebra. These include an efficient version of the Fast Multipole Method in one dimension and fast algorithms for the evaluation, integration and differentiation of Lagrange polynomial interpolants. Several numerical examples are used to illustrate the efficiency of the approach, and to compare the performances of the two sets of nonuniform FFT algorithms.