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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 8 — Aug. 1, 1999
  • pp: 1892–1908

Multidimensional fast Fourier transform algorithm for signals with arbitrary symmetries

R. Bernardini, G. Cortelazzo, and G. A. Mian  »View Author Affiliations


JOSA A, Vol. 16, Issue 8, pp. 1892-1908 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001892


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Abstract

A multidimensional fast Fourier transform (FFT) algorithm is presented for signals with arbitrary symmetries and periodic on arbitrary lattices. Applications that can benefit from such an algorithm include Volterra filtering and analysis of x-ray diffraction data. The presented algorithm exploits signal redundancy to achieve a computational complexity of N log N, where N is the number of independent samples. To the authors’ knowledge, this is the only FFT that makes the frequency domain computation of Volterra filtering more convenient than the time domain approach.

© 1999 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(000.4430) General : Numerical approximation and analysis

History
Original Manuscript: August 10, 1998
Revised Manuscript: March 29, 1999
Manuscript Accepted: March 29, 1999
Published: August 1, 1999

Citation
R. Bernardini, G. Cortelazzo, and G. A. Mian, "Multidimensional fast Fourier transform algorithm for signals with arbitrary symmetries," J. Opt. Soc. Am. A 16, 1892-1908 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-8-1892


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References

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  2. G. Sicuranza, “Quadratic filters for signal processing,” Proc. IEEE 80, 1262–1285 (1992). [CrossRef]
  3. R. Bernardini, G. M. Cortelazzo, G. A. Mian, “A fast convolution technique for Volterra filtering,” in Proceedings of the Workshop on Nonlinear Digital Signal Processing (Neos Marmaras, Halkidiki, Greece, 1995), pp. 363–366.
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  8. R. Bernardini, G. M. Cortelazzo, G. A. Mian, “A new multidimensional FFT based on one-dimensional decompositions,” submitted to IEEE Trans. Circuits Syst. II.
  9. R. Bernardini, G. M. Cortelazzo, G. A. Mian, “A new technique for twiddle-factors elimination in multidimensional FFT,” IEEE Trans. Signal Process. 42, 2176–2178 (1994). [CrossRef]

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