Generalized Discrete Entropic Uncertainty Relations on Linear Canonical Transform

Show more

References

[1] R. Ishii and K. Furukawa, “The Uncertainty Principle in Discrete Signals,” IEEE Transactions on Circuits and Systems, Vol. 33, No. 10, 1986, pp. 1032-1034.

[2] L. C. Calvez and P. Vilbe, “On the Uncertainty Principle in Discrete Signals,” IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing, Vol. 39, No. 6, 1992, pp. 394-395.
http://dx.doi.org/10.1109/82.145299

[3] S. Shinde and M. G. Vikram, “An Uncertainty Principle for Real Signals in the Fractional Fourier Transform Domain,” IEEE Transactions of Signal Processing, Vol. 49, No. 11, 2001, pp. 2545-2548.
http://dx.doi.org/10.1109/78.960402

[4] G. L. Xu, X. T. Wang and X. G. Xu, “Generalized Entropic Uncertainty Principle on Fractional Fourier Transform,” Signal Processing, Vol. 89, No. 12, 2009, pp. 2692-2697.

http://dx.doi.org/10.1016/j.sigpro.2009.05.014

[5] R. Tao, B. Deng and Y. Wang, “Theory and Application of the Fractional Fourier Transform,” Tsinghua University Press, Beijing, 2009.

[6] S. C. Pei and J. J. Ding, “Eigenfunctions of Fourier and Fractional Fourier Transforms with Complex Offsets and Parameters,” IEEE Trans Circuits and Systems-I: Regular Papers, Vol. 54, No. 7, 2007, pp. 1599-1611.

[7] T. M. Cover and J. A. Thomas, “Elements of Information Theory,” 2nd Edition, John Wiley &Sons, Inc., 2006.

[8] H. Maassen, “A Discrete Entropic Uncertainty Relation,” Quantum Probability and Applications, Springer-Verlag, New York, 1988, pp. 263-266.

[9] C. E. Shannon, “A Mathematical Theory of Communication,” The Bell System Technical Journal, Vol. 27, 1948, pp. 379-656.

http://dx.doi.org/10.1002/j.1538-7305.1948.tb01338.x

[10] A. Rényi, “On Measures of Information and Entropy,” Proceedings of the 4th Berkeley Symposium on Mathematics, Statistics and Probability, 1960, p. 547.

[11] G. Hardy, J. E. Littlewood and G. Pólya, “Inequalities,” 2nd Edition, Press of University of Cambridge, Cambridge, 1951.

[12] D. Amir, T. M. Cover and J. A. Thomas, “Information Theoretic Inequalities,” IEEE Transactions on Information Theory, Vol. 37, No. 6, 2001, pp. 1501-1508.

[13] A. Dembo, T. M. Cover and J. A. Thomas, “Information Theoretic Inequalities,” IEEE Transactions on Information Theory, Vol. 37, No. 6, 1991, pp. 1501-1518.
http://dx.doi.org/10.1109/18.104312

[14] G. L. Xu, X. T. Wang and X. G. Xu, “The Logarithmic, Heisenberg’s and Short-Time Uncertainty Principles Associated with Fractional Fourier Transform,” Signal Processing, Vol. 89, No. 3, 2009, pp. 339-343.

http://dx.doi.org/10.1016/j.sigpro.2008.09.002

[15] G. L. Xu, X. T. Wang and X. G. Xu, “Generalized Uncertainty Principles Associated with Hilbert Transform Signal,” Image and Video Processing, 2013.

[16] G. L. Xu, X. T. Wang and X. G. Xu, “The Entropic Uncertainty Principle in Fractional Fourier Transform Domains,” Signal Processing, Vol. 89, No. 12, 2009, pp. 2692-2697.

http://dx.doi.org/10.1016/j.sigpro.2009.05.014

[17] A. Stern, “Sampling of Linear Canonical Transformed Signals,” Signal Processing, Vol. 86, No. 7, 2006, pp. 1421-1425. http://dx.doi.org/10.1016/j.sigpro.2005.07.031

[18] G. L. Xu, X. T. Wang and X. G. Xu, “Three Cases of Uncertainty Principle for Real Signals in Linear Canonical Transform Domain,” IET Signal Processing, Vol. 3, No. 1, 2009, pp. 85-92.

http://dx.doi.org/10.1049/iet-spr:20080019

[19] A. Stern, “Uncertainty Principles in Linear Canonical Transform Domains and Some of Their Implications in Optics,” Journal of the Optical Society of America, Vol. 25, No. 3, 2008, pp. 647-652.

http://dx.doi.org/10.1364/JOSAA.25.000647

[20] G. L. Xu, X. T. Wang and X. G. Xu, “Uncertainty Inequalities for Linear Canonical Transform,” IET Signal Processing, Vol. 3, No. 5, 2009, pp. 392-402,.

http://dx.doi.org/10.1049/iet-spr.2008.0102