Fractional power spectrum

IEEE Transactions on Signal Processing

Volumn 56, Issue 9, 2008, Pages 4199-4206

  Tao, Ran ^a   Zhang, Feng ^a   Wang, Yue ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Fractional correlation function; Fractional Fourier transform; Fractional power spectrum; Fractional white noise

Indexed keywords

CHIRP SIGNALS; DETERMINISTIC PROCESS; FRACTIONAL CORRELATION FUNCTION; FRACTIONAL FOURIER DOMAINS; FRACTIONAL FOURIER TRANSFORM; FRACTIONAL POWER SPECTRUM; FRACTIONAL WHITE NOISE; POTENTIAL APPLICATIONS; SIMULATION RESULTS; STATIONARY PROCESS; SYSTEM IDENTIFICATIONS;

DIGITAL SIGNAL PROCESSING; MINES; PARAMETER ESTIMATION; POWER SPECTRUM; SPECTRUM ANALYSIS; WHITE NOISE;

FOURIER TRANSFORMS;

EID: 65449161002     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.925579     Document Type: Article

References (36)

1. J. A. Cadzow, "Spectral estimation: An overdetermined rational model equation approach," Proc. IEEE, vol. 70, pp. 907-939, Sep. 1982.
2. B. Picinbono, Random Signals and Systems. Englewood Cliffs, NJ: Prentice-Hall, 1993.
3. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise. New York: Wiley-IEEE, 1987.
4. L. B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Process., vol. 42, pp. 3084-3091, Nov. 1994.
5. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform With Applications in Optics and Signal Processing. New York: Wiley, 2000.
6. D. Mendlovic, H. M. Ozaktas, and A. W. Lohmann, "Fractional correlation," Appl. Opt., vol. 34, pp. 303-309, Jan. 1995.
7. V. Namias, "The fractional order Fourier transform and its application to quantum mechanics," J. Inst. Math. Appl., vol. 25, pp. 241-265, 1980.
8. M. A. Kutay, H. M. Ozaktas, O. Arikan, and L. Onural, "Optimal filtering in fractional Fourier domain," IEEE Trans. Signal Process. vol. 45, pp. 1129-1143, May 1997.
9. A. I. Zayed, "On the relationship between the Fourier transform and fractional Fourier transform," IEEE Signal Process. Lett., vol. 3, pp. 310-311, Dec. 1996.
10. A. W. Lohmann, "Image rotation, Wigner rotation, and the fractional Fourier transform," J. Opt. Soc. Amer. A., vol. 10, pp. 2181-2186, 1993.
11. 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 transform," J. Opt. Soc. Amer. A. vol. 11, pp. 547-559, 1994.
12. A. W. Lohmann and B. H. Soffer, "Relationship between the Radon-Wigner and the fractional Fourier transform," J. Opt. Soc. Amer. A., vol. 11, pp. 1798-1801, 1994.
13. D. Mustard, "The fractional Fourier transform and the Wigner distribution," J. Austral. Math. Soc. B-Appl. Math., vol. 38, pp. 209-219, 1996.
14. S. C. Pei and J. J. Ding, "Relations between fractional operations and time-frequency distributions, and their applications," IEEE Trans. Signal Process., vol. 49, pp. 1638-1655, Aug. 2001.
15. C. Candan, M. A. Kutay, and H. M. Ozaktas, "The discrete fractional Fourier transform," IEEE Trans. Signal Process., vol. 48, pp. 1329-1337, May 2000.
16. H. M. Ozaktas and O. Aytur, "Fractional Fourier domains," Signal Processing, vol. 46, pp. 119-124, 1995.
17. P. Kraniauskas, G. Cariolaro, and T. Erseghe, "Method for defining a class of fractional operations," IEEE Trans. Signal Process., vol. 46, pp. 2804-2807, Oct. 1998.
18. G. Cariolaro, T. Erseghe, P. Kraniauskas, and N. Laurenti, "A unified framework for the fractional Fourier transform," IEEE Trans. Signal Process., vol. 46, pp. 3206-3219, Dec. 1998.
19. L. B. Almeida, "Product and convolution theorems for the fractional Fourier transform," IEEE Signal Process. Lett., vol. 4, pp. 15-17, Jan. 1997.
20. A. I. Zayed, "A convolution and product theorem for the fractional Fourier transform," IEEE Signal Process. Lett., vol. 5, pp. 101-103, Apr. 1998.
21. X. Xia, "On bandlimited signals with fractional Fourier transform," IEEE Signal Process. Lett., vol. 3, pp. 72-74, Mar. 1996.
22. T. Erseghe, P. Kraniauskas, and G. Cariolaro, "Unified fractional Fourier transform and sampling theorem," IEEE Trans. Signal Process. vol. 47, pp. 3419-3423, Dec. 1999.
23. S. C. Pei and J. J. Ding, "Simplified fractional Fourier transforms," J. Opt. Soc. Amer. A., vol. 17, pp. 2355-2367, 2000.
24. M. F. Erden, M. A. Kutay, and H. M. Ozaktas, "Repeated filtering in consecutive fractional Fourier domains and its application to signal restoration," IEEE Trans. Signal Process., vol. 47, pp. 1458-1462, May 1999.
25. Z. Zalevsky and D. Mendlovic, "Fractional Wiener filter," Appl. Opt., vol. 35, pp. 3930-3936, 1996.
26. M. A. Kutay, H.M. Ozaktas, O. Arikan, and L. Onural, "Optimal image restoration with the fractional Fourier transform," J. Opt. Soc. Amer. A., vol. 15, pp. 825-833, 1998.
27. M. F. Erden and H. M. Ozaktas, "Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains," J. Opt. Soc. Amer. A., vol. 15, pp. 1647-1657, 1998.
28. Y. Chen, R. Sun, and A. Zhou, "An improved hurst parameter estimator based on fractional Fourier transform," in Proc. ASME Design Eng. Tech. Conf., Las Vegas, NV, Sep. 4-7, 2007, 3rd ASME Symp. Fractional Derivatives and Their Applications (FDTA'07), part of the 6th ASME International Conf. Multibody Systems, Nonlinear Dynamics, and Control (MSNDC).
29. H. M. Ozaktas, O. Arikan, M. A. Kutay, and G. Bozdagi, "Digital computation of the fractional Fourier transform," IEEE Trans. Signal Process., vol. 44, pp. 2141-2150, Sep. 1996.
30. H. M. Ozaktas and D. Mendlovic, "Fractional Fourier optics," J. Opt. Soc. Amer. A., vol. 12, pp. 743-751, 1995.
31. Y. Chen, R. Sun, and A. Zhou, "An overview of fractional order signal processing (FOSP) techniques," in Proc ASME Design Eng. Tech. Conf. Las Vegas, NV, Sep. 4-7, 2007, 3rd ASME Symp. Fractional Derivatives and Their Applications (FDTA'07), part of the 6th ASME Int. Conf. Multibody Systems, Nonlinear Dynamics, and Control (MSNDC).
32. C. L. Nikias and M. Shao, Signal Processing With Alpha-Stable Distributions and Applications. New York: Wiley, 1995.
33. M. Shao and C. L. Nikias, "Signal processing with fractional lower order moments: Stable processes and their applications," Proc. IEEE vol. 81, pp. 986-1010, Jul. 1993.
34. A. C. McBride and F. H. Kerr, "On Namias's fractional Fourier transforms," IMA J. Appl. Math., vol. 39, pp. 159-175, 1987.
35. H. M. Ozaktas, B. Barshan, and D. Mendlovic, "Convolution and filtering in fractional Fourier domain," Opt. Rev., vol. 1, pp. 15-16, 1994.
36. Y. Chen, Dr YangQuan Chen's FRFT (Fractional Fourier Transform) Web Pages [Online]. Available: http://mechatronics.ece.usu.edu/foc/FRFT/.