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Volumn 89, Issue 3, 2009, Pages 339-343

The logarithmic, Heisenberg's and short-time uncertainty principles associated with fractional Fourier transform

Author keywords

Fractional Fourier transform (FRFT); Heisenberg's uncertainty principle; Short time FRFT (STFRFT)

Indexed keywords

DIGITAL SIGNAL PROCESSING; MATHEMATICAL TRANSFORMATIONS; MINES;

EID: 56049121172     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sigpro.2008.09.002     Document Type: Article
Times cited : (52)

References (25)
  • 1
    • 0035503193 scopus 로고    scopus 로고
    • An uncertainty principle for real signals in the fractional Fourier transform domain
    • Shinde S., and Vikram M.G. An uncertainty principle for real signals in the fractional Fourier transform domain. IEEE Trans. Signal Process. 49 11 (2001) 2545-2548
    • (2001) IEEE Trans. Signal Process. , vol.49 , Issue.11 , pp. 2545-2548
    • Shinde, S.1    Vikram, M.G.2
  • 2
    • 0006486256 scopus 로고
    • Uncertainty principle invariant under fractional Fourier transform
    • Mustard D. Uncertainty principle invariant under fractional Fourier transform. J. Aust. Math. Soc. Ser. B 33 (1991) 180-191
    • (1991) J. Aust. Math. Soc. Ser. B , vol.33 , pp. 180-191
    • Mustard, D.1
  • 4
    • 56049125364 scopus 로고    scopus 로고
    • K.K. Selig, Uncertainty principles revisited, Technische Universitat Munchen, Technical Report, 2001. [Online]. Available: 〈http://www-lit.ma.tum.de/veroeff/quel/010.47001.pdf〉.
    • K.K. Selig, Uncertainty principles revisited, Technische Universitat Munchen, Technical Report, 2001. [Online]. Available: 〈http://www-lit.ma.tum.de/veroeff/quel/010.47001.pdf〉.
  • 5
    • 0029369313 scopus 로고
    • Fractional Fourier domains
    • Ozaktas H.M., and Aytur O. Fractional Fourier domains. Signal Process. 46 (Sept. 1995) 119-124
    • (1995) Signal Process. , vol.46 , pp. 119-124
    • Ozaktas, H.M.1    Aytur, O.2
  • 6
    • 0039768601 scopus 로고    scopus 로고
    • The uncertainty principle: a mathematical survey
    • Folland G.B., and Sitaram A. The uncertainty principle: a mathematical survey. J. Fourier Anal. Appl. 3 3 (1997) 207-238
    • (1997) J. Fourier Anal. Appl. , vol.3 , Issue.3 , pp. 207-238
    • Folland, G.B.1    Sitaram, A.2
  • 7
    • 0029389835 scopus 로고
    • Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transform
    • Aytur O., and Ozaktas H.M. Non-orthogonal domains in phase space of quantum optics and their relation to fractional Fourier transform. Opt. Commun. 120 (1995) 166-170
    • (1995) Opt. Commun. , vol.120 , pp. 166-170
    • Aytur, O.1    Ozaktas, H.M.2
  • 10
    • 2442623404 scopus 로고    scopus 로고
    • The uncertainty principle: global, local, or both?
    • Loughlin P.J., and Cohen L. The uncertainty principle: global, local, or both?. IEEE Trans. Signal Process. 52 5 (2004) 1218-1227
    • (2004) IEEE Trans. Signal Process. , vol.52 , Issue.5 , pp. 1218-1227
    • Loughlin, P.J.1    Cohen, L.2
  • 11
    • 0001542262 scopus 로고
    • A note on entropy
    • Hirschman Jr. I.I. A note on entropy. Am. J. Math. 79 1 (January 1957) 152-156
    • (1957) Am. J. Math. , vol.79 , Issue.1 , pp. 152-156
    • Hirschman Jr., I.I.1
  • 13
    • 1842817380 scopus 로고
    • Entropic uncertainty relations in quantum mechanics
    • Accardi L., and von Waldenfels W. (Eds), Springer, Berlin
    • Birula I.B. Entropic uncertainty relations in quantum mechanics. In: Accardi L., and von Waldenfels W. (Eds). Quantum Probability and Applications II, Lecture Notes in Mathematics vol. 1136 (1985), Springer, Berlin 90
    • (1985) Quantum Probability and Applications II, Lecture Notes in Mathematics , vol.1136 , pp. 90
    • Birula, I.B.1
  • 14
    • 0001491241 scopus 로고
    • Pitt's inequality and the uncertainty principle
    • Beckner W. Pitt's inequality and the uncertainty principle. Proc. Am. Math. Soc. 123 6 (June 1995) 1897-1905
    • (1995) Proc. Am. Math. Soc. , vol.123 , Issue.6 , pp. 1897-1905
    • Beckner, W.1
  • 15
    • 56049126054 scopus 로고    scopus 로고
    • W. Beckner, Pitt's inequality with sharp error estimates, Analysis of PDEs (math. AP), [Online]. Available: 〈http://arxiv.org/abs/math/0701939〉, accepted for publication.
    • W. Beckner, Pitt's inequality with sharp error estimates, Analysis of PDEs (math. AP), [Online]. Available: 〈http://arxiv.org/abs/math/0701939〉, accepted for publication.
  • 16
    • 56049120897 scopus 로고    scopus 로고
    • W. Beckner, Pitt's inequality with sharp convolution estimates, eprint arXiv:math/0701939, [Online]. Available: 〈http://adsabs.harvard.edu/abs/2007math......1939B〉.
    • W. Beckner, Pitt's inequality with sharp convolution estimates, eprint arXiv:math/0701939, [Online]. Available: 〈http://adsabs.harvard.edu/abs/2007math......1939B〉.
  • 17
    • 0027652515 scopus 로고
    • Fractional Fourier transforms and their optical implementation (I)
    • Mendlovic D., and Ozaktas H.M. Fractional Fourier transforms and their optical implementation (I). J. Opt. Soc. Am. Assoc. 10 10 (1993) 1875-1881
    • (1993) J. Opt. Soc. Am. Assoc. , vol.10 , Issue.10 , pp. 1875-1881
    • Mendlovic, D.1    Ozaktas, H.M.2
  • 18
    • 0027740848 scopus 로고
    • Fractional Fourier transforms and their optical implementation (II)
    • Ozaktas H.M., and Mendlovic D. Fractional Fourier transforms and their optical implementation (II). J. Opt. Soc. Am. A 10 10 (1993) 2522-2531
    • (1993) J. Opt. Soc. Am. A , vol.10 , Issue.10 , pp. 2522-2531
    • Ozaktas, H.M.1    Mendlovic, D.2
  • 19
    • 77958407025 scopus 로고
    • The fractional order Fourier transform and its application to quantum mechanics
    • Namias V. The fractional order Fourier transform and its application to quantum mechanics. J. Inst. Math. Appl. 25 (1980) 241-265
    • (1980) J. Inst. Math. Appl. , vol.25 , pp. 241-265
    • Namias, V.1
  • 20
    • 0035424885 scopus 로고    scopus 로고
    • Relations between Fractional operations and time-frequency distributions, and their applications
    • Pei S.C., and Ding J.J. Relations between Fractional operations and time-frequency distributions, and their applications. IEEE Trans. Signal Proc. 49 8 (2001) 1638-1655
    • (2001) IEEE Trans. Signal Proc. , vol.49 , Issue.8 , pp. 1638-1655
    • Pei, S.C.1    Ding, J.J.2
  • 21
    • 0035309420 scopus 로고    scopus 로고
    • Two-dimensional affine generalized fractional Fourier transform
    • Pei S.C., and Ding J.J. Two-dimensional affine generalized fractional Fourier transform. IEEE Trans. Signal Process. 49 4 (2001) 878-897
    • (2001) IEEE Trans. Signal Process. , vol.49 , Issue.4 , pp. 878-897
    • Pei, S.C.1    Ding, J.J.2
  • 22
    • 0033702254 scopus 로고    scopus 로고
    • The uncertainty principles of windowed wave functions
    • Cohen L. The uncertainty principles of windowed wave functions. Opt. Commun. 179 (2000) 221-229
    • (2000) Opt. Commun. , vol.179 , pp. 221-229
    • Cohen, L.1
  • 23
    • 4243455901 scopus 로고
    • Operational approach to phase-space measurements in quantum mechanics
    • Wódkiewicz K. Operational approach to phase-space measurements in quantum mechanics. Phys. Rev. Lett. 52 13 (1984) 1064-1067
    • (1984) Phys. Rev. Lett. , vol.52 , Issue.13 , pp. 1064-1067
    • Wódkiewicz, K.1
  • 24
    • 0141996361 scopus 로고    scopus 로고
    • Time-frequency signal analysis based on the windowed fractional Fourier transform
    • Stankovic L., Alieva T., and Bastiaans M.J. Time-frequency signal analysis based on the windowed fractional Fourier transform. Signal Process. 83 (2003) 2459-2468
    • (2003) Signal Process. , vol.83 , pp. 2459-2468
    • Stankovic, L.1    Alieva, T.2    Bastiaans, M.J.3
  • 25
    • 0038320362 scopus 로고    scopus 로고
    • Fractional Fourier transform of the Gaussian and fractional domain signal support
    • Capus C., and Brown K. Fractional Fourier transform of the Gaussian and fractional domain signal support. IEE Proc. Vision Image Signal Process. 150 2 (2003) 99-106
    • (2003) IEE Proc. Vision Image Signal Process. , vol.150 , Issue.2 , pp. 99-106
    • Capus, C.1    Brown, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.