Abstract

The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT’s) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT. This improved DFRFT provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties.

© 1997 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. C. McBride and F. H. Kerr, IMA J. Appl. Math. 39, 159 (1987).
  2. R. G. Dorsch, A. W. Lohmann, Y. Bitran, and D. Mendlovic, Appl. Opt. 33, 7599 (1994).
  3. A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).
  4. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, Appl. Opt. 34, 303 (1995).
  5. A. W. Lohmann and B. H. Soffer, J. Opt. Soc. Am. A 11, 1798 (1994).
  6. D. Mendlovic, Z. Zalevsky, A. W. Lohmann, and R. G. Dorsch, Opt. Commun. 126, 14 (1996).
  7. G. Sansone, Orthogonal Function, Vol. 9 of Pure and Applied Mathematics (Interscience, New York, 1959).
  8. B. W. Dickinson and K. Steiglitz, IEEE Trans. Acoust. Speech Signal Process ASSP-30, 25 (1982).
  9. C. C. Shih, Opt. Commun. 118, 495 (1995).
  10. B. Santhanam and J. H. McClellan, IEEE Trans. Signal Process. 42, 994 (1996).
  11. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).
  12. Z. T. Deng, H. J. Caulfield, and M. Schamschula, Opt. Lett. 21, 1430 (1996).
  13. H. M. Ozaktas, B. Barshan, D. Mendlovic, and L. Onural, J. Opt. Soc. Am. A 11, 547 (1994).
  14. J. H. McClellan and T. W. Parks, IEEE Trans. Audio Electroacoust. AU-20, 66 (1972).
  15. P. M. Morse and H. Feschbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1416.

1996

D. Mendlovic, Z. Zalevsky, A. W. Lohmann, and R. G. Dorsch, Opt. Commun. 126, 14 (1996).

Z. T. Deng, H. J. Caulfield, and M. Schamschula, Opt. Lett. 21, 1430 (1996).

1995

1994

1993

1959

G. Sansone, Orthogonal Function, Vol. 9 of Pure and Applied Mathematics (Interscience, New York, 1959).

1953

P. M. Morse and H. Feschbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1416.

Arikan, O.

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).

Barshan, B.

Bitran, Y.

Bozdagi, G.

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).

Caulfield, H. J.

Deng, Z. T.

Dickinson, B. W.

B. W. Dickinson and K. Steiglitz, IEEE Trans. Acoust. Speech Signal Process ASSP-30, 25 (1982).

Dorsch, R. G.

D. Mendlovic, Z. Zalevsky, A. W. Lohmann, and R. G. Dorsch, Opt. Commun. 126, 14 (1996).

R. G. Dorsch, A. W. Lohmann, Y. Bitran, and D. Mendlovic, Appl. Opt. 33, 7599 (1994).

Feschbach, H.

P. M. Morse and H. Feschbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1416.

Kerr, F. H.

A. C. McBride and F. H. Kerr, IMA J. Appl. Math. 39, 159 (1987).

Kutay, M. A.

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).

Lohmann, A. W.

McBride, A. C.

A. C. McBride and F. H. Kerr, IMA J. Appl. Math. 39, 159 (1987).

McClellan, J. H.

J. H. McClellan and T. W. Parks, IEEE Trans. Audio Electroacoust. AU-20, 66 (1972).

B. Santhanam and J. H. McClellan, IEEE Trans. Signal Process. 42, 994 (1996).

Mendlovic, D.

Morse, P. M.

P. M. Morse and H. Feschbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1416.

Onural, L.

Ozaktas, H. M.

Parks, T. W.

J. H. McClellan and T. W. Parks, IEEE Trans. Audio Electroacoust. AU-20, 66 (1972).

Sansone, G.

G. Sansone, Orthogonal Function, Vol. 9 of Pure and Applied Mathematics (Interscience, New York, 1959).

Santhanam, B.

B. Santhanam and J. H. McClellan, IEEE Trans. Signal Process. 42, 994 (1996).

Schamschula, M.

Shih, C. C.

C. C. Shih, Opt. Commun. 118, 495 (1995).

Soffer, B. H.

Steiglitz, K.

B. W. Dickinson and K. Steiglitz, IEEE Trans. Acoust. Speech Signal Process ASSP-30, 25 (1982).

Zalevsky, Z.

D. Mendlovic, Z. Zalevsky, A. W. Lohmann, and R. G. Dorsch, Opt. Commun. 126, 14 (1996).

Appl. Opt.

IEEE Trans. Acoust. Speech Signal Process

B. W. Dickinson and K. Steiglitz, IEEE Trans. Acoust. Speech Signal Process ASSP-30, 25 (1982).

IEEE Trans. Audio Electroacoust.

J. H. McClellan and T. W. Parks, IEEE Trans. Audio Electroacoust. AU-20, 66 (1972).

IEEE Trans. Signal Process.

B. Santhanam and J. H. McClellan, IEEE Trans. Signal Process. 42, 994 (1996).

H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, IEEE Trans. Signal Process. 44, 2141 (1996).

IMA J. Appl. Math.

A. C. McBride and F. H. Kerr, IMA J. Appl. Math. 39, 159 (1987).

J. Opt. Soc. Am. A

Opt. Commun.

D. Mendlovic, Z. Zalevsky, A. W. Lohmann, and R. G. Dorsch, Opt. Commun. 126, 14 (1996).

C. C. Shih, Opt. Commun. 118, 495 (1995).

Opt. Lett.

Other

G. Sansone, Orthogonal Function, Vol. 9 of Pure and Applied Mathematics (Interscience, New York, 1959).

P. M. Morse and H. Feschbach, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), p. 1416.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics