Generalization of the fractional hilbert transform

IEEE Signal Processing Letters

Volumn 15, Issue , 2008, Pages 365-368

  Tao, Ran ^a   Li, Xue Mei ^a,b   Wang, Yue ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

^b BEIJING ELECTRONIC SCIENCE AND TECHNOLOGY INSTITUTE   (China)

Author keywords

Fractional fourier transform; Fractional Hilbert transform; Single sideband (SSB)

Indexed keywords

FRACTIONAL FOURIER TRANSFORM; FRACTIONAL FOURIER TRANSFORMS; FRACTIONAL HILBERT TRANSFORM; HILBERT TRANSFORM; MODULATION SYSTEMS; REAL SIGNALS; SINGLE-SIDEBAND (SSB);

HILBERT SPACES; MINES;

FOURIER TRANSFORMS;

EID: 67650124164     PISSN: 10709908     EISSN: None     Source Type: Journal    
DOI: 10.1109/LSP.2008.919814     Document Type: Article

References (14)

1. D. Gabor, "Theory of communications," J. Inst. Elect. Eng., vol. 93, pp. 429-457, Nov. 1946.
2. L. B. Almeida, "The fractional Fourier transform and time-frequency representations," IEEE Trans. Signal Process., vol. 42, no. 11, pp. 3084-3091, Nov. 1994.
3. R. Tao, B. Deng, and Y. Wang, "Research progress of the fractional Fourier transform in signal processing," Sci. China: Series F Inf. Sci., vol. 49, pp. 1-25, Feb. 2006.
4. A. I. Zayed, "A convolution and product theorem for the fractional Fourier transform," IEEE Signal Process. Lett., vol. 5, no. 4, pp. 101-103, Apr. 1998.
5. R. Tao, B. Z. Li, and Y. Wang, "Spectral analysis and reconstruction for periodic non-uniformly sampled signals in fractional Fourier domain," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 3541-3547, Jul. 2007.
6. V. Namias, "The fractional order Fourier transform and its applications to quantum mechanics," J. Inst. Math. Appl., vol. 25, pp. 241-265, Apr. 1980.
7. T. Alieva, V. Lopez, F. Aguillo-Lopez, and L. B. Almeida, "The fractional Fourier transform in optical propagation problems," J. Mod. Opt., vol. 41, pp. 1037-1040, May 1994.
8. K. Kohlmann, "Corner detection in natural images based on the 2-d Hilbert transform," Signal Process., vol. 48, pp. 225-234, Feb. 1996.
9. A. Lohmann, D. Mendlovic, and Z. Zalevsky, "Fractional Hilbert transform," Opt. Lett., vol. 21, pp. 281-283, Feb. 1996.
10. A. I. Zayed, "Hilbert transform associated with the fractional Fourier transform," IEEE Signal Process. Lett., vol. 5, no. 8, pp. 206-208, Aug. 1998.
11. C. C. Tseng and S. C. Pei, "Design and application of discrete-time fractional Hilbert transformer," IEEE Trans. Circuits Syst. II, vol. 47, no. 12, pp. 1529-1533, Dec. 2000.
12. X. G. Xia, "On bandlimited signals with fractional Fourier transform," IEEE Signal Process. Lett., vol. 3, no. 3, pp. 72-74, Mar. 1996.
13. S. C. Pei and J. J. Ding, "Saving the bandwidth in the fractional domain by generalized Hilbert transform pair relations," in Proc. IEEE Int. Symp. Circuits and Systems, May 2003, vol. 4, pp. 89-92.
14. A. I. Zayed and A. Garcia, "New sampling formulae for the fractional Fourier transform," Signal Process., vol. 77, pp. 111-114, Aug. 1999.