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Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT)

Iterative algorithm for nonuniform inverse fast Fourier transform (NU-IFFT)

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A nonuniform inverse fast Fourier transform (NU-IFFT) for nonuniformly sampled data is realised by combining the conjugate-gradient fast Fourier transform (CG-FFT) method with the newly developed nonuniform fast Fourier transform (NUFFT) algorithms. An example application of the algorithm in computational electromagnetics is presented.

Inspec keywords: fast Fourier transforms; electromagnetism; iterative methods

Other keywords: fast Fourier transform; nonuniform inverse FFT; nonuniformly sampled data; computational electromagnetics; conjugate-gradient FFT; iterative algorithm; IFFT; nonuniform FFT algorithms

Subjects: Other numerical methods; Integral transforms; Interpolation and function approximation (numerical analysis)

References

    1. 1)
      • G. Beylkin . On fast Fourier transform of functions with singularities. Appl. Comput. Harmonic Analysis , 363 - 381
    2. 2)
      • M.F. Cátedra , R.P. Torres , J. Basterrechea , E. Gago . (1995) The CG-FFT method: Applicationof signal processing techniques to electromagnetics.
    3. 3)
      • A. Dutt , V. Rokhlin . Fast Fourier transform for nonequispaced data. SIAM J. Sci. Comput. , 1368 - 1393
    4. 4)
      • Q.H. Liu , N. Nguyen . An accurate algorithm for nonuniform fast Fouriertransforms (NUFFT's). IEEE Microw. Guid. Wave Lett. , 18 - 20
    5. 5)
      • J.W. Cooley , J.W. Tukey . Algorithm for the machine computation of complexFourier series. Math. Comp. , 297 - 301
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