Abstract and Applied Analysis

Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms

Yong-Gang Li, Bing-Zhao Li, and Hua-Fei Sun

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The Heisenberg uncertainty principle of harmonic analysis plays an important role in modern applied mathematical applications, signal processing and physics community. The generalizations and extensions of the classical uncertainty principle to the novel transforms are becoming one of the most hottest research topics recently. In this paper, we firstly obtain the uncertainty principle for Wigner-Ville distribution and ambiguity function associate with the linear canonical transform, and then the n -dimensional cases are investigated in detail based on the proposed Heisenberg uncertainty principle of the n -dimensional linear canonical transform.

Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 470459, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412276986

Digital Object Identifier
doi:10.1155/2014/470459

Mathematical Reviews number (MathSciNet)
MR3212428

Zentralblatt MATH identifier
07022440

Citation

Li, Yong-Gang; Li, Bing-Zhao; Sun, Hua-Fei. Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms. Abstr. Appl. Anal. 2014 (2014), Article ID 470459, 9 pages. doi:10.1155/2014/470459. https://projecteuclid.org/euclid.aaa/1412276986


Export citation

References

  • S. A. Collins, “Lens-system difraction integral written in terms of matrix optics,” The Journal of the Optical Society of America, vol. 60, pp. 1168–1177, 1970.
  • J. Zhao, R. Tao, and Y. Wang, “Multi-channel filter banks associated with linear canonical transform,” Signal Processing, vol. 93, pp. 695–705, 2013.
  • B.-Z. Li, R. Tao, and Y. Wang, “Frames in linear canonical transform domain,” Acta Electronica Sinica, vol. 35, no. 7, pp. 1387–1390, 2007.
  • Y.-L. Liu, K.-I. Kou, and I.-T. Ho, “New sampling formulae for non-bandlimited signals associated with linear canonical transform and nonlinear Fourier atoms,” Signal Processing, vol. 90, no. 3, pp. 933–945, 2010.
  • A. Stern, “Sampling of compact signals in offset linear canonical transform domains,” Signal, Image and Video Processing, vol. 1, no. 4, pp. 359–367, 2007.
  • J. J. Healy and J. T. Sheridan, “Sampling and discretization of the linear canonical transform,” Signal Processing, vol. 89, no. 4, pp. 641–648, 2009.
  • B. M. Hennelly and J. T. Sheridan, “Fast numerical algorithm for the linear canonical transform,” Journal of the Optical Society of America A: Optics, Image Science, and Vision, vol. 22, no. 5, pp. 928–937, 2005.
  • A. Koç, H. M. Ozaktas, C. Candan, and M. A. Kutay, “Digital computation of linear canonical transforms,” IEEE Transactions on Signal Processing, vol. 56, no. 6, pp. 2383–2394, 2008.
  • R.-F. Bai, B.-Z. Li, and Q.-Y. Cheng, “Wigner-Ville distribution associated with the linear canonical transform,” Journal of Applied Mathematics, vol. 2012, Article ID 740161, 14 pages, 2012.
  • T. W. Che, B. Z. Li, and T. Z. Xu, “The ambiguity function associated with the linear canonical transform,” EURASIP Journal on Advances in Signal Processing, vol. 2012, article 138, 2012.
  • G. B. Folland and A. Sitaram, “The uncertainty principle: a mathematical survey,” The Journal of Fourier Analysis and Applications, vol. 3, no. 3, pp. 207–238, 1997.
  • K. K. Sharma and S. D. Joshi, “Uncertainty principle for real signals in the linear canonical transform domains,” IEEE Transactions on Signal Processing, vol. 56, no. 7, pp. 2677–2683, 2008.
  • J. Zhao, R. Tao, Y.-L. Li, and Y. Wang, “Uncertainty principles for linear canonical transform,” IEEE Transactions on Signal Processing, vol. 57, no. 7, pp. 2856–2858, 2009.
  • G. L. Xu, X. T. Wang, and X. G. Xu, “Three uncertainty relations for real signals associated with linear canonical transform,” IET Signal Processing, vol. 3, no. 1, pp. 85–92, 2009.
  • G. L. Xu, X. T. Wang, and X. G. Xu, “Uncertainty inequalities for linear canonical transform,” IET Signal Processing, vol. 3, no. 5, pp. 392–402, 2009.
  • K.-I. Kou, R.-H. Xu, and Y.-H. Zhang, “Paley-Wiener theorems and uncertainty principles for the windowed linear canonical transform,” Mathematical Methods in the Applied Sciences, vol. 35, no. 17, pp. 2122–2132, 2012.
  • J. J. Ding and S. C. Pei, “Heisenberg's uncertainty principle for the 2-D nonseparable linear canonical transforms,” Signal Processing, vol. 93, pp. 1027–1043, 2013.
  • M. Moshinsky and C. Quesne, “Linear canonical transformations and their unitary representations,” Journal of Mathematical Physics, vol. 12, pp. 1772–1780, 1971.
  • K. B. Wolf, Integral Transforms in Science and Engineering, vol. 11, chapter 9: canonical transforms, Plenum Press, NewYork, NY, USA, 1979.
  • R. Tao, B. Deng, and Y. Wang, Fractional Fourier Transform and Its Applications, Tsinghua University Press, Beijing, China, 2009.
  • T. Z. Xu and B. Z. Li, Linear Canonical Transform and Its Applications, Science Press, Beijing, China, 2013.
  • L. Debnath, “Recent developments in the Wigner-Ville distribution and time-frequency signal analysis,” Proceedings of the Indian National Science Academy A: Physical Sciences, vol. 68, no. 1, pp. 35–56, 2002.
  • S.-C. Pei and J.-J. Ding, “Relations between fractional operations and time-frequency distributions, and their applications,” IEEE Transactions on Signal Processing, vol. 49, no. 8, pp. 1638–1655, 2001.
  • H. Zhao, Q.-W. Ran, J. Ma, and L.-Y. Tan, “Linear canonical ambiguity function and linear canonical transform moments,” Optik, vol. 122, no. 6, pp. 540–543, 2011.
  • L. Debnath, Wavelet Transforms and their Applications, Birkhäuser, Boston, Mass, USA, 2002.
  • L. Debnath, Wavelet Transforms and Time-Frequency Signal Analysis, Birkhäuser, Boston, Mass, USA, 2002. \endinput