## Multidimensional fast Fourier transform algorithm for signals with arbitrary symmetries

JOSA A, Vol. 16, Issue 8, pp. 1892-1908 (1999)

http://dx.doi.org/10.1364/JOSAA.16.001892

Enhanced HTML Acrobat PDF (324 KB)

### 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* 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

Sort: Year | Journal | Reset

### References

- J. Cooley, J. W. Tukey, “An algorithm for the machine computation of the complex Fourier series,” Math. Comput. 19, 297–301 (1965). [CrossRef]
- G. Sicuranza, “Quadratic filters for signal processing,” Proc. IEEE 80, 1262–1285 (1992). [CrossRef]
- 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.
- V. Kucera, Discrete Linear Control: The Polynomial Equation (Wiley, New York, 1979).
- D. Dudgeon, R. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1984).
- P. Vaidyanathan, Multirate Systems and Filter Banks (Prentice-Hall, Englewood Cliffs, N.J., 1993).
- N. Jacobson, Basic Algebra I (Freeman, New York, 1985).
- R. Bernardini, G. M. Cortelazzo, G. A. Mian, “A new multidimensional FFT based on one-dimensional decompositions,” submitted to IEEE Trans. Circuits Syst. II.
- 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]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.