Discrete fractional Fourier transform based on orthogonal projections

IEEE Transactions on Signal Processing

Volumn 47, Issue 5, 1999, Pages 1335-1348

  Pei, Soo Chang ^b   Yeh, Min Hung ^a,c   Tseng, Chien Cheng ^d,e  

^a IEEE

^b NATIONAL TAIWAN UNIVERSITY   (Taiwan)

^c ALETHEIA UNIVERSITY   (Taiwan)

^d HWA HSIA INSTITUTE OF TECHNOLOGY   (Taiwan)

^e NATIONAL KAOHSIUNG UNIVERSITY OF APPLIED SCIENCES   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS;

DISCRETE FRACTIONAL FOURIER TRANSFORM; ORTHOGONAL PROJECTION METHODS; SIGNAL ANALYSIS;

SIGNAL PROCESSING;

EID: 0032669485     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/78.757221     Document Type: Article

References (31)

1. R. N. Bracewell The Fourier Transform and Its Applications 2nd ed. New York: McGraw-Hill 1986.
2. A. C. McBride and F. H. Kerr "On Namias' fractional Fourier transforms" IMA J. Appl. Math. vol. 39 pp. 159-175 1987.
3. V. Namias "The fractional order Fourier transform and its application to quantum mechanics" J. Inst. Math. Applicat. vol. 25 pp. 241-265 1980.
4. F. Hlawatsch and G. F. Bourdeaux-Bartels "Linear and quadratic time-frequency signal representations" IEEE Signal Processing Mag. vol. 9 pp. 21-67 Apr. 1992.
5. H. M. Ozaktas B. Barshan and D. Mendlovic "Convolution and filtering in fractional Fourier domain" Opt. Rev. vol. 1 pp. 15-16 1994.
6. H. M. Ozaktas B. Barshan D. Mendlovic and L. Onural "Convolution filtering and multiplexing in fractional Fourier domains and their relationship to chirp and wavelet transforms" J. Opt. Soc. Amer. A vol. 11 pp. 547-559 Feb. 1994.
7. R. G. Dorsch A. W. Lohmann Y. Bitran and D. Mendlovic "Chirp filtering in the fractional Fourier domain" Appl. Opt. vol. 33 pp. 7599-7602 1994.
8. A. W. Lohmann and B. H. Soffer "Relationships between the Radon-Wigner and fractional Fourier transforms" J. Opt. Soc. Amer. A vol. 11 pp. 1798-1801 June 1994.
9. L. B. Almeida "The fractional Fourier transform and time-frequency representation" IEEE Trans. Signal Processing vol. 42 pp. 3084-3091 Nov. 1994.
10. D. Mendlovic H. M. Ozaktas and A. W. Lohmann "Fractional correlation" Appl. Opt. vol. 34 pp. 303-309 Jan. 1995.
11. H. M. Ozaktas N. Erkaya and M. A. Kutay "Effect of fractional Fourier transformation on time-frequency distributions belonging to the Cohen class" IEEE Signal Processing Lett. vol. 3 pp. 40-41 Feb. 1996.
12. D. Dragonman "Fractional Wigner distribution function" J. Opt. Soc. Amer. A vol. 13 pp. 474-478 Mar. 1996.
13. H. M. Ozaktas "Fractional Fourier domains" Signal Process. vol. 46 pp. 119-124 1995.
14. D. Mendlovic and H. M. Ozaktas "Fractional Fourier transformations and their optical implementation - I" J. Opt. Soc. Amer. A vol. 10 pp. 1875-1881 1993.
15. Fractional Fourier transformations and their optical implementation - II" J. Opt. Soc. Amer. A vol. 10 pp. 2522-2531 1993.
16. H. M. Ozaktas O. Arikan M. A. Kutay and G. Bozdagi "Digital computation of the fractional Fourier transform" IEEE Trans. Signal Processing vol. 44 pp. 2141-2150 Sept. 1996.
17. B. Santhanam and J. H. McClellan "The discrete rotational Fourier transform" IEEE Trans. Signal Processing. vol. 42 pp. 994-998 Apr. 1996.
18. G. Sansone Orthogonal Functions. New York Interscience 1959.
19. B. A. Weisburn T. W. Parks and R. G. Shenoy "Separation of transient signals" in Proc. 6th IEEE DSP Workshop Oct. 1994 pp. 199-203.
20. B. W. Dickinson and K. Steiglitz "Eigenvectors and functions of the discrete Fourier transform" IEEE Trans. Acoust. Speech Signal Processing vol. ASSP-30 pp. 25-31 Feb. 1982.
21. J. H. McClellan and T. W. Parks "Eigenvalue and eigenvector decomposition of the discrete Fourier transform" IEEE Trans. Audio Electroacoust. vol. AU-20 pp. 66-74 Mar. 1972.
22. G. Cincotti F. Gori and M. Santarsiero "Generalized self-Fourier functions" J. Phys. vol. 25 pp. 1191-1194 1992.
23. A. V. Oppenheim Discrete-Time Signal Processing. Englewood Cliffs NJ: Prentice-Hall 1989.
24. S. C. Pei and M. H. Yeh "Discrete fractional Fourier transform" in Proc. IEEE Int. Symp. Circuits Syst. May 1996 pp. 536-539.
25. Improved discrete fractional Fourier transform" Opt. Lett. vol. 22 pp. 1047-1049 July 15 1997.
26. Two dimensional discrete fractional Fourier transform" Signal Process. vol. 67 pp. 99-108 1998.
27. S. C. Pei C.-C. Tseng M.-H. Yeh and J. J. Shyu "Discrete fractional Hartley and Fourier transforms" IEEE Trans. Circuits Syst. II vol. 45 pp. 665-675 1998.
28. P. M. Morse and H. Feschbach Methods of Theoretical Physics. New York: McGraw-Hill 1953 p. 1416.
29. S. H. Friedberg A. J. Insel and L. E. Spence Linear Algebra. Englewood Cliffs NJ: Prentice-Hall 1989.
30. G. H. Golub and C. F. Van Loan Matrix Computations. Baltimore MD: Johns Hopkins Univ. Press 1989.
31. O. Arikan M. A. Kutay H. M. Ozaktas and O. K. Aademir "The discrete fractional Fourier transform" in Proc. IEEE Int. Symp. Time-Freq. Time-Scale Anal. June 1996 pp. 205-207.