Some uncertainty principles for time-frequency transforms of the cohen class

IEEE Transactions on Signal Processing

Volumn 53, Issue 2 I, 2005, Pages 523-527

  Korn, Peter ^a  

^a MAX PLANCK INSTITUTE FOR METEOROLOGY   (Germany)

Author keywords

Cohen transform; Essential support; Hardy's uncertainty principle; Inversion of Cohen transforms; Time frequency concentration; Uncertainty principle

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FOURIER TRANSFORMS; FREQUENCY DOMAIN ANALYSIS; INTEGRAL EQUATIONS; THEOREM PROVING;

COHEN TRANSFORM; HARDY UNCERTAINTY PRINCIPLE; TIME FREQUENCY TRANSFORM; UNCERTAINTY PRINCIPLE;

SIGNAL PROCESSING;

EID: 13244263041     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2004.840738     Document Type: Article

References (18)

1. L. Cohen, "Generalized phase-space distribution functions," J. Math. Phys., vol. 7, 1966.
2. P. Flandrin, Time-Frequency/Time-Scale Analysis. San Diego, CA: Academic, 1999.
3. L. Cohen, Time-Frequency Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1995.
4. K. H. Gröchenig, Foundations of Time-Frequency Analysis. Boston, MA: Birhkäuser, 2000.
5. H. Dym and H. P. McKean, Fourier Series and Integrals. New York: Academic, 1972.
6. D. L. Donoho and P. Stark, "Uncertainty principles and signal recovery," SIAM J. Appl. Math., vol. 49, no. 3, pp. 906-931, 1989.
7. P. Flandrin, "Maximum signal energy concentration in a time-frequency domain," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. New York, 1988, pp. 2176-2179.
8. I. Daubechies, "Time-frequency localization operators: a geometric phase space approach," IEEE Trans. Inf. Theory, vol. 34, no. 4, pp. 605-612, Aug. 1988.
9. J. Ramanathan and P. Topiwala, "Time-frequency localization via the Weyl correspondence," SIAM J. Math. Anal., vol. 24, no. 5, pp. 1378-1393, 1993.
10. J. Ramanathan and P. Topiwala, "Time-frequency localization and the spectogram," Appl. Comput. Harm. Anal., vol. 1, pp. 209-215, 1994.
11. A. J. E. M. Janssen, "Proof of a conjecture on the supports of Wigner distributions," J. Fourier Anal. Appl, vol. 4, pp. 723-726, 1998.
12. J. C. T. Pool, "Mathematical aspects of the Weyl correspondence," J. Math. Phys., vol. 7, pp. 66-76, 1966.
13. G. Folland, Harmonic Analysis in Phase Space. Princeton, NJ: Princeton Univ. Press, 1989.
14. R. G. Shenoy and T. W. Parks, "The Weyl correspondence and time-frequency analysis," IEEE Trans. Signal Process., vol. 42, no. 2, pp. 318-331, Feb. 1994.
15. M. G. Cowling and J. F. Price, "Bandwith versus time-concentration: the Heisenberg-Pauli-Weyl inequality," SIAM J. Math. Anal., vol. 15, pp. 151-165, 1984.
16. F. L. Nazarov, "Local estimates of exponential poynomials and their application to inequalities of uncertainty principle type," St. Petersburg Math. J., 1994.
17. J. Bertrand and P. Bertrand, "A tomographic approach to Wigner's function," Found. Phys., vol. 1,7, no. 4, pp. 397-405, 1987.
18. J. C. Wood and D. T. Barry, "Tomographic time-frequency analysis and its application toward time varying filtering and adaptive kernel design for multicomponent linear-FM signals," IEEE Trans. Signal Process. vol. 42, no. 8, pp. 2094-2104, Aug. 1994.