Parseval relationship of samples in the fractional fourier transform domain

Journal of Applied Mathematics

Volumn 2012, Issue , 2012, Pages

  Li, Bing Zhao ^a   Xu, Tian Zhou ^a  

^a BEIJING INSTITUTE OF TECHNOLOGY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84864929467     PISSN: 1110757X     EISSN: 16870042     Source Type: Journal    
DOI: 10.1155/2012/428142     Document Type: Article

References (32)

1. Ozaktas H. M., Kutay M. A., Zalevsky Z., The Fractional Fourier Transform with Applications in Optics and Signal Processing 2001 New York, NY, USA John Wiley Sons
2. Tao R., Deng B., Wang Y., Fractional Fourier Transform and Its Applications 2009 Beijing, China Tsinghua University Press
3. Jacob R., Thomas T., Unnikrishnan A., Applications of fractional Fourier transform in sonar signal processing IETE Journal of Research 2009 55 1 16 27
4. Yang D., Xiao D., Zhang L., The parameters estimation and the feature extraction of underwater transient signal Proceedings of the IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC '11) October 2011 1 4
5. Feng Y., Tao R., Wang Y., Modeling and characteristic analysis of underwater acoustic signal of the accelerating propeller Science China Information Sciences 2012 55 2 270 280
6. Lohmann A. W., Soffer B. H., Relationships between the Radon-Wigner and fractional Fourier transforms Journal of the Optical Society of America A 1994 11 6 1798 1801
7. Zayed A. I., On the relationship between the Fourier and fractional Fourier transforms IEEE Signal Processing Letters 1996 3 12 310 311 (Pubitemid 126527116)
8. Xia X.-G., On bandlimited signals with fractional Fourier transform IEEE Signal Processing Letters 1996 3 3 72 74 (Pubitemid 126534572)
9. Ozaktas H. M., Ankan O., Alper Kutay M., Bozdagi G., Digital computation of the fractional Fourier transform IEEE Transactions on Signal Processing 1996 44 9 2141 2150 (Pubitemid 126776500)
10. Pei S.-C., Yeh M.-H., Tseng C.-C., Discrete fractional Fourier transform based on orthogonal projections IEEE Transactions on Signal Processing 1999 47 5 1335 1348
11. Pei S.-C., Ding J.-J., Closed-form discrete fractional and affine Fourier transforms IEEE Transactions on Signal Processing 2000 48 5 1338 1353
12. Candan C., Kutay M. A., Ozaktas H. M., The discrete fractional Fourier transform IEEE Transactions on Signal Processing 2000 48 5 1329 1337
13. Serbes A., Durak-Ata L., The discrete fractional Fourier transform based on the DFT matrix Signal Processing 2011 91 3 571 581
14. Wei D. Y., Ran Q. W., Li Y. M., Ma J., Tan L. Y., Fractionalisation of an odd time odd frequency DFT matrix based on the eigenvectors of a novel nearly tridiagonal commuting matrix IET Signal Processing 2011 5 2 150 156
15. Erseghe T., Kraniauskas P., Cariolaro G., Unified fractional Fourier transform and sampling theorem IEEE Transactions on Signal Processing 1999 47 12 3419 3423 (Pubitemid 30531537)
16. Wei D., Ran Q., Li Y., Generalized sampling expansion for bandlimited signals associated with the fractional Fourier transform IEEE Signal Processing Letters 2010 17 6 595 598
17. Saxena R., Singh K., Fractional Fourier transform: a novel tool for signal processing Journal of the Indian Institute of Science 2005 85 1 11 26 (Pubitemid 40785331)
18. Tao R., Deng B., Wang Y., Research progress of the fractional Fourier transform in signal processing Science in China Series F: Information Sciences 2006 49 1 1 25 (Pubitemid 44598410)
19. Zayed A. I., Hilbert transform associated with the fractional Fourier transform IEEE Signal Processing Letters 1998 5 8 206 208 (Pubitemid 128556811)
20. Zayed A. I., A convolution and product theorem for the fractional Fourier transform IEEE Signal Processing Letters 1998 5 4 101 103 (Pubitemid 128556806)
21. Almeida L. B., Product and convolution theorems for the fractional Fourier transform IEEE Signal Processing Letters 1997 4 1 15 17 (Pubitemid 127554931)
22. Shinde S., Gadre V. M., An uncertainty principle for real signals in the fractional Fourier transform domain IEEE Transactions on Signal Processing 2001 49 11 2545 2548 (Pubitemid 33048425)
23. Li B.-Z., Tao R., Xu T.-Z., Wang Y., The Poisson sum formulae associated with the fractional Fourier transform Signal Processing 2009 89 5 851 856
24. Tao R., Li B.-Z., Wang Y., Spectral analysis and reconstruction for periodic nonuniformly sampled signals in fractional Fourier domain IEEE Transactions on Signal Processing 2007 55 7, part 1 3541 3547 (Pubitemid 47018836)
25. Tao R., Li Y.-L., Wang Y., Short-time fractional Fourier transform and its applications IEEE Transactions on Signal Processing 2010 58 5 2568 2580
26. Lima J. B., Campello De Souza R. M., The fractional Fourier transform over finite fields Signal Processing 2012 92 2 465 476
27. Irarrazaval P., Lizama C., Parot V., Sing-Long C., Tejos C., The fractional Fourier transform and quadratic field magnetic resonance imaging Computers Mathematics with Applications 2011 62 3 1576 1590
28. Kilbas A. A., Luchko Yu. F., Martnez H., Trujillo J. J., Fractional Fourier transform in the framework of fractional calculus operators Integral Transforms and Special Functions 2010 21 9-10 779 795
29. Oppenheim A. V., Schafer R. W., Digital Signal Processing 1989 Englewood Cliffs, NJ, USA Prentice-Hall
30. Marvasti F. A., Chuande L., Parseval relationship of nonuniform samples of one- and two-dimensional signals IEEE Transactions on Acoustics, Speech, and Signal Processing 1990 38 6 1061 1063
31. Luthra A., Extension of Parsevals relation to nonuniform samples IEEE Transactions on Signal Processing 1988 36 12 1909 1991
32. Pei S.-C., Yeh M.-H., Two dimensional discrete fractional Fourier transform Signal Processing 1998 67 1 99 108 (Pubitemid 128415755)