Tomograms and other transforms: A unified view

Journal of Physics A: Mathematical and General

Volumn 34, Issue 40, 2001, Pages 8321-8332

  Man'ko, M A ^a,b   Man'ko, V I ^a,b   Mendes, R Vilela ^b,c  

^a LEBEDEV PHYSICAL INSTITUTE   (Russian Federation)

^b BIELEFELD UNIVERSITY   (Germany)

^c UNIVERSITY OF LISBON   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012404477     PISSN: 03054470     EISSN: None     Source Type: Journal    
DOI: 10.1088/0305-4470/34/40/309     Document Type: Article

References (32)

1. Pouarikas A D (ed) 1996 The Transforms and Applications Handbook (Boca Raton, FL: CRC Press)
2. Wolf K-B 1979 Integral Transforms in Science and Engineering (New York: Plenum)
3. Fourier J B J 1988 Théorie Analytique de la Chaleur ed G Darbous Oeuvres de Fourier Tome Premier (Paris: Gauthiers-Villars)
4. Combes J M, Grossmann A and Tchamitchian Ph (ed) 1990 Wavelets 2nd edn (Berlin: Springer)
5. Daubechies I 1990 The wavelet transform: time-frequency localization and signal analysis IEEE Trans. Inf. Theory 36 961-1005
6. Chui C K (ed) 1992 Wavelets: A Tutorial. Theory and Applications vol 2 (Boston: Academic)
7. Wigner E 1932 On the quantum correction for thermodynamic equilibrium Phys. Rev. 40 749-59
8. Ville J 1948 Théorie et applications de la notion de signal analytique Cables Transm. A 2 61-74
9. Cohen L 1966 Generalized phase-space distribution functions J. Math. Phys. 7 781-806
10. Qian S and Chen D 1965 Joint Time-Frequency Analysis (Englewood Cliffs, NJ: Prentice-Hall)
11. Woods J C and Barry D T 1994 Linear signal synthesis using the Radon-Wigner transform IEEE Trans. Signal Process. 42 2105-11
12. Granieri S, Furlan W D, Saavedra G and Andrés P 1997 Radon-Wigner display: a compact optical implementation with a single varifocal lens Appl. Opt. 36 8363-9
13. Man'ko V I and Mendes R V 1999 Noncommutative time-frequency tomography Phys. Lett. A 263 53-9
14. Glauber R J 1963 Coherent and incoherent states of the radiation fields Phys. Rev. 131 2766-88 Glauber R J 1963 Photon correlations Phys. Rev. Lett. 10 84-6
15. Glauber R J 1963 Coherent and incoherent states of the radiation fields Phys. Rev. 131 2766-88 Glauber R J 1963 Photon correlations Phys. Rev. Lett. 10 84-6
16. Sudarshan E C G 1963 Equivalence of semiclassical and quantum-mechanical descriptions of statistical light beams Phys. Rev. Lett. 10 277-9
17. Husimi K 1940 Some formal properties of the density matrix Proc. Phys. Math. Soc. Japan 22 264-314
18. Kano Y 1965 A new phase-space distribution function in the statistical theory of the electromagnetic field J. Math. Phys. 6 1913-5
19. Cahill K E and Glauber R J 1969 Density operators and quasiprobability distributions Phys. Rev. 177 1882-902
20. Bertrand J and Bertrand P 1992 A class of affine Wigner functions with extended covariance properties J. Math. Phys. 33 2515-27
21. Goncalvés P and Baraniuk R J 1996 A pseudo-Bertrand distribution for time-scale analysis IEEE Signal Process. Lett. 3 82-4
22. Flandrin P and Goncalvés P 1994 From wavelets to time-scale energy distributions Recent Advances in Wavelet Analysis ed L L Schumaker and J Webb (New York: Academic) pp 309-34
23. Cohen L 1993 The scale representation IEEE Trans. Signal Process. 41 3275-92
24. Reed M and Simon B 1980 Functional Analysis (San Diego: Academic) ch 8
25. Cohen L 1989 Time-frequency distributions - a review Proc. IEEE 77 941-81
26. Dodonov V V and Man'ko V I 1989 Invariants and evolution of nonstationary quantum systems Proc. P N Lebedev Physical Institute vol 183 (Commack, NY: Nova Science)
27. Ali T, Atakishiyev N M, Chumakov S M and Wolf K-B 2000 The Wigner function for general Lie groups and the wavelet transform Ann. Inst. Henri Poincaré 1 685-714
28. Atakishiyev N M, Chumakov S M and Wolf K-B 1998 Wigner distribution function for finite systems J. Math. Phys. 139 6244-61
29. Nieto L M, Atakishiyev N M, Chumakov S M and Wolf K-B 1998 Wigner distribution function for Euclidean systems J. Phys. A: Math. Gen. 31 3875-95
30. Mancini S, Tombesi P and Man'ko V I 1997 Density matrix from photon number tomography Europhys. Lett. 37 79-83
31. Wallentowitz S and Vogel W 1996 Unbalanced homodyning for quantum state measurements Phys. Rev. A 53 4528-33
32. Banaszek K and Wodkiewicz K 1996 Direct probing of quantum phase space by photon counting Phys. Rev. Lett. 76 4344-7