The Hyperbolic Class of Quadratic Time-Frequency Representations Part I: Constant-Q Warping, the Hyperbolic Paradigm, Properties, and Members

IEEE Transactions on Signal Processing

Volumn 41, Issue 12, 1993, Pages 3425-3444

  Papandreou, Antonia ^a   Boudreaux Bartels, G Faye ^a   Hlawatsch, Franz ^b  

^a UNIVERSITY OF RHODE ISLAND   (United States)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER TRANSFORMS; FREQUENCY SHIFT KEYING; INVARIANCE; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; SIGNAL FILTERING AND PREDICTION;

COHEN'S CLASS; CONSTANT Q WARPING; HYPERBOLIC CLASS; QUADRATIC TIME FREQUENCY REPRESENTATIONS; WAVELET TRANSFORM;

SIGNAL PROCESSING;

EID: 0027798109     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.258084     Document Type: Article

References (37)

1. F. Hlawatsch and G. F. Boudreaux-Bartels, “Linear and quadratic time-frequency signal representations,” IEEE Signal Processing Mag., vol. 9, pp. 21–67, Apr. 1992.
2. L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys., vol. 7, pp. 781–786, 1966.
3. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “The Wigner distribution—A tool for time-frequency signal analysis, Part III: Relations with other time-frequency signal transformations,” Philips J. Res., vol. 35, pp. 372–389, 1980.
4. F. Hlawatsch, “Duality and classification of bilinear time-frequency signal representations,” IEEE Trans. Signal Processing, vol. 39, pp. 1564–1574, July 1991.
5. O. Rioul and M. Vetterli, “Wavelets and signal processing,” IEEE Signal Processing Mag., vol. 8, pp. 14–38, Oct. 1991.
6. O. Rioul and P. Flandrin, “Time-scale energy distributions: A general class extending wavelet transforms,” IEEE Trans. Signal Processing, vol. 40, pp. 1746–1757, July 1992.
7. J. Bertrand and P. Bertrand, “Time-frequency representations of broad-band signals,” Proc. IEEE ICASSP-88, New York, Apr. 1988, pp. 2196–2199.
8. J.Bertrand P. Bertrand “Affine time-frequency distributions,” in B. Boashash Ed., Time-Frequency Signal Analysis—Methods and Applications. Melbourne, Australia: Longman-Cheshire, 1991.
9. P. Flandrin, “Sur une classe generale d’extensions affines de la distribution de Wigner-Ville,” 13eme Coll. GRETSI, Juan-les-Pins, France, Sept. 1991.
10. P. Flandrin, “Scale-invariant Wigner spectra and self-similarity,” Proc. EUSIPCO-90, Barcelona, Spain, Sept. 1990, pp. 149–152.
11. C. Braccini and G. Gambardella, “Form-invariant linear filtering: Theory and applications,” IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-34, pp. 1612–1628, Dec. 1986.
12. J. M. Speiser, “Wideband ambiguity function,” IEEE Trans. Informat. Theory, vol. 13, pp. 122–123, 1967.
13. R. A. Altes, “Wideband, proportional-bandwidth Wigner-Ville analysis,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1005–1012, June 1990.
14. J. Bertrand and P. Bertrand, “Representations temps-frequence des signaux,” C.R. Acad. Sci. Paris, vol. 299, pp. 635–638, 1984.
15. J. Bertrand, P. Bertrand, and J. P. Ovarlez, “Discrete Mellin transform for signal analysis,” Proc. IEEE ICASSP-90, Albuquerque, NM, pp. 1603–1606, April 1990.
16. J. Bertrand and P. Bertrand, “A class of affine Wigner functions with extended covariance properties,” J. Math. Phys., vol. 33, pp. 2515–2527, 1992.
17. R. A. Altes and E. L. Titlebaum, “Bat signals as optimally Doppler tolerant waveforms,” J. Acoust. Soc. Am., vol. 48, pp. 1014–1020, Oct. 1970.
18. N. M. Marinovic, “The Wigner distribution and the ambiguity function: Generalizations, enhancement, compression and some applications,” Ph.D. dissertation, City University of New York, 1986.
19. A. Papandreou, F. Hlawatsch, and G. F. Boudreaux-Bartels, “Quadratic time-frequency distributions: The new hyperbolic class and its intersection with the affine class,” Sixth SP Workshop on Statistical Signal and Array Processing, Victoria, BC, Canada, Oct. 1992, pp. 26–29.
20. R. G. Shenoy and T. W. Parks, “Affine Wigner distributions,” Proc. IEEE ICASSP-92, vol. 5, San Francisco, CA, Mar. 1992, pp. 185–188.
21. F. Hlawatsch, A. Papandreou, and G. F. Boudreaux-Bartels, “The hyperbolic class of quadratic time-frequency representations, Part II,” to be submitted.
22. A. Papandreou, F. Hlawatsch, and G. F. Boudreaux-Bartels, “A unified framework for the Bertrand distribution and the Altes distribution: The new hyperbolic class of quadratic time-frequency distributions,” Proc. IEEE Symp. Time-Frequency and Time-Scale Analysis, Victoria, BC, Canada, Oct. 1992, pp. 27–30.
23. F. Hlawatsch and P. Flandrin, “The interference structure of the Wigner distribution and related time-frequency signal representations,” to appear in W. Mecklenbrauker, Ed., The Wigner Distribution-Theory and Applications in Signal Processing. New York: Elsevier, 1994.
24. R. G. Baraniuk and D. L. Jones, “Unitary equivalence: A new twist on signal processing,” submitted to IEEE Trans. Signal Processing.
25. R. G. Baraniuk and D. L. Jones, “Warped wavelet bases: Unitary equivalence and signal processing,” Proc. IEEE ICASSP-93, Minneapolis, MN, Apr. 1993, vol. 3, pp. 320–323.
26. P. Flandrin, “Some features of time-frequency representations of multicomponent signals,” Proc. IEEE ICASSP-84, San Diego, CA, pp. 41B.4.1-4, Mar. 1984.
27. L. Cohen and T. E. Posch, “Generalized ambiguity functions,” Proc. IEEE ICASSP-85, Tampa, FL, Mar. 1985, pp. 1033–1036.
28. J. P. Ovarlez, “La transformation de Mellin: Un outil pour l'analyse des signaux a large bande,” These Univ. Paris 6 1992.
29. F. Hlawatsch and R. L. Urbanke, “Bilinear time-frequency representations of signals: The shift-scale invariant class,” to appear in IEEE Trans. Signal Processing, vol. 42, Feb. 1994.
30. F. Hlawatsch, A Papandreou, and G. F. Boudreaux-Bartels, “The power classes of quadratic time-frequency representations: A generalization of the affine and hyperbolic classes,” Proc. 27th Annual Asilomar Conf., Nov. 1993, Pacific Grove, CA.
31. T. A. C. M. Claasen and W. F. G. Mecklenbrauker, “The Wigner distribution—A tool for time-frequency signal analysis, Part I: Continuous-time signals,” Philips J. Res., vol. 35, pp. 217–250, 1980.
32. A. J. E. M. Janseen, “On the locus and spread of pseudo-density functions in the time-frequency plane,” Philips J. Res., vol. 37, no. 3, pp. 79–110, 1982.
33. P. Flandrin and W. Martin, “Sur les conditions physiques assurant l’unicite de la representation de Wigner-Ville comme representation temps-frequence,” Neuvieme Coll, sur le Traitement du Signal et ses Applications (GRETSI-83), Nice, France, May 1983.
34. F. Hlawatsch, “Regularity and unitarity of bilinear time-frequency signal representations,” IEEE Trans. Informat. Theory, vol. 38, pp. 82-94, Jan. 1992.
35. F. Hlawatsch, A. Papandreou, and G. F. Boudreaux-Bartels, “Regularity and unitarity of affine and hyperbolic time-frequency representations,” Proc. IEEE ICASSP-93, vol. 3, Minneapolis, MN, Apr. 1993, pp. 245–248.
36. J.P. Ovarlez, J. Bertrand, and P. Bertrand, “Computation of affine time-frequency distributions using the fast Mellin transform,” Proc. IEEE ICASSP-92, vol. 5, San Francisco, CA, 1992, pp. 117-120.
37. L. Cohen, “A general approach for obtaining joint representations in signal analysis and an application to scale,” Proc. SPIE Advanced Signal Processing Algorithms, Architectures, and Implementations II, vol. 1566, pp. 109-133, July 1991.