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A group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval -,. 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 N + N (1/) ) arithmetic operations, where is the precision of computations and N is the number of nodes. The efficiency of the approach is illustrated by several numerical examples.
Dutt et al. (1993) studied this question.