Nonuniform fast Fourier transforms using min-max interpolation
Fessler, J.A.
Sutton, B.P.
Dept. of Electr. Eng., Comput. Sci. & Biomed. Eng., Michigan Univ., Ann Arbor, MI, USA;
This paper appears in: Signal Processing, IEEE Transactions on
Publication Date: Feb 2003
Volume: 51,
Issue: 2
On page(s): 560- 574
ISSN: 1053-587X
INSPEC Accession Number: 7515014
Digital Object Identifier: 10.1109/TSP.2002.807005
Current Version Published: 2003-01-22
Abstract
The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.
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