Wigner distribution representation and analysis of audio signals: An illustrated tutorial review

AES: Journal of the Audio Engineering Society

Volumn 47, Issue 12, 1999, Pages 1043-1053

  Preis, Douglas ^a   Georgopoulos, Voula Chris ^b,c  

^a TUFTS UNIVERSITY   (United States)

^b Ohio University   (United States)

^c TECHNOLOGICAL EDUCATIONAL INSTITUTE OF PATRAS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER TRANSFORMS; FREQUENCY DOMAIN ANALYSIS; SPECTRUM ANALYSIS; TIME DOMAIN ANALYSIS;

WIGNER DISTRIBUTIONS;

ACOUSTIC SIGNAL PROCESSING;

EID: 0033279871     PISSN: 00047554     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. T. A. C. M. Claasen and W. F. G. Mecklenbräuker, "The Wigner Distribution: A Tool for Time-Frequency Analysis," in Proc. IEEE Acoustics, Speech and Signal Processing Society L'Aquila Workshop (L'Aquila, Italy, 1980).
2. T. A. C. M. Claasen and W. F. G. Mecklenbräuker, "The Wigner Distribution - A Tool for Time-Frequency Analysis, Parts I-III," Philips J. Res., vol. 35, pp. 217-250, 276-300, 372-389 (1980).
3. E. P. Wigner, "On the Quantum Correction for Thermodynamic Equilibrium," Phys. Rev., vol. 40, pp. 749-759 (1932).
4. J. Ville, "Theorie et applications de la notion de signal analytique," Cables et Transmissions, vol. 2A, no. 1, pp. 61-74 (1948).
5. P. M. Woodward, Probability and Information Theory with Application to Radar (Pergamon, London, 1953).
6. P. Y. Ktonas and N. Papp, "Instantaneous Envelope and Phase Extraction from Real Signals: Theory, Implementation, and an Application to EEG Analysis," Signal Process., vol. 2, pp. 373-385 (1980).
7. L. B. White and B. Boashash, "On Estimating the Instantaneous Frequency of a Gaussian Random Signal by Use of the Wigner-Ville Distribution," IEEE Trans. Acoust., Speech, Signal Process., vol. 36, pp. 417-420 (1988).
8. P. Rao and F. J. Taylor, "Estimation of Instantaneous Frequency Using the Discrete Wigner Distribution," Electron. Lett., vol. 26, pp. 246-248 (1990).
9. K. M. Wong and Q. Jin, "Estimation of the Time-Varying Frequency of a Signal: The Cramer-Rao Bound and the Application of Wigner Distribution," IEEE Trans. Acoust., Speech, Signal Process., vol. 38, pp. 519-536 (1990).
10. B. Boashash and L. B. White, "Instantaneous Frequency Estimation and Automatic Time-Varying Filtering," in Proc. ICAASP '90 (1990), pp. 1221-1224.
11. B. Boashash and P. O'Shea, "Use of the Cross Wigner-Ville Distribution for Estimation of Instantaneous Frequency," IEEE Trans. Signal Process., vol. 41, pp. 1439-1445 (1993).
12. K. S. Riedel, "Kernel Estimation of the Instantaneous Frequency," IEEE Trans. Signal Process., vol. 42, pp. 2644-2648 (1994).
13. L. J. Stankovic and S. Stankovic, "An Analysis of Instantaneous Frequency Representation Using Time-Frequency Distributions-Generalized Wigner Distribution," IEEE Trans. Signal Process., vol. 43, pp. 549-552 (1995).
14. V. C. Georgopoulos and D. Preis, "A Comparison of Computational Methods for Instantaneous Frequency and Group Delay of Discrete-Time Signals," Dept. of Electrical Engineering, Tufts University, Medford, MA, Tech. Rep. TR-EEDSP01-93 (1993).
15. V. C. Georgopoulos and D. Preis, "A Comparison of Computational Methods for Instantaneous Frequency and Group Delay of Discrete-Time Signals," J. Audio Eng. Soc., vol. 46, pp. 152-163 (1998 Mar.).
16. E. F. Velez and R. G. Absher, "Spectral Estimation Based on the Wigner-Ville Representation," Signal Process., vol. 20, pp. 325-346 (1990).
17. B. Boashash, "Time-Frequency Signal Analysis," in Advances in Spectrum Analysis and Array Processing, S. Haykin, Ed. (Prentice-Hall, Englewood Cliffs, NJ, 1991), pp. 418-517.
18. J. J. Eggermont and G. M. Smith, "Characterizing Auditory Neurons Using the Wigner and Rihaczek Distributions: A Comparison," J. Acoust. Soc. Am., vol. 87, pp. 246-259 (1990).
19. C. P. Janse and A. J. M. Kaizer, "Time-Frequency Distributions of Loudspeakers: The Application of the Wigner Distribution," J. Audio Eng. Soc., vol. 31, pp. 198-223 (1983 Apr.).
20. D. Preis, F. Hlawatsch, P. J. Bloom, and J. A. Deer, "Wigner Distribution Analysis of Filters with Perceptible Phase Distortion," J. Audio Eng. Soc. (Communications), vol. 35, pp. 1004-1012 (1987 Dec.).
21. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
22. V. C. Georgopoulos and D. Preis, "Analysis of PSK- and FSK-Modulated Signals Using Time-Frequency Information", Dept. of Electrical Engineering, Tufts University, Medford, MA, Tech. Rep. TR-EEDSPO1-94 (1994).
23. L. Cohen, Time-Frequency Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1995).
24. L. Cohen and T. Posch, "Positive Time-Frequency Distribution Functions," IEEE Trans. Acoust., Speech, Signal Process., vol. 33, pp. 31-37 (1985).
25. P. J. Loughlin, J. W. Pitton, and L. E. Atlas, "Construction of Positive Time-Frequency Distributions," IEEE Trans. Signal Process., vol. 42, pp. 2697-2705 (1994).
26. J. R. Fonollosa and C. L. Nikias, "A New Positive Time-Frequency Distribution," in Proc. IEEE IC-ASSP-94 (1994), pp. 301-304.
27. J. R. Fonollosa, "Positive Time-Frequency Distributions Based on Joint Marginal Constraints," IEEE Trans. Signal Process., vol. 44, p. 2086 (1996).
28. H. I. Choi and W. J. Williams, "Improved Time-Frequency Representation of Multicomponent Signal Using Exponential Kernels," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, pp. 862-871 (1989).
29. P. J. Loughlin, J. W. Pitton, and B. Hanaford, "Fast Approximations to Positive Time-Frequency Distributions with Applications,"in Proc. ICASSP-95 (Detroit, MI, 1995), pp. 1009-1012.
30. R. G. Baraniuk and D. L. Jones, "A Signal-Dependent Time-Frequency Representation: Optimal Kernel Design," IEEE Trans. Signal Process., vol. 41, pp. 1589-1602 (1993).
31. R. G. Baraniuk and D. L. Jones, "Signal-Dependent Time-Frequency Analysis Using a Radially Gaussian Kernel," Signal Process., vol. 32, pp. 263-284 (1993).
32. D. L. Jones and R. G. Baraniuk, "An Adaptive Optimal-Kernel Time-Frequency Representation," IEEE Trans. Signal Process., vol. 43, pp. 2361-2371 (1995).
33. R. G. Baraniuk, "Nonlinear Wigner-Ville Spectrum Estimation Using Wavelet Soft-Thresholding," in Proc. SPIE Symp. on OE/Aerospace Sensing and Dual Use Photonics, Mathematical Imaging: Wavelet Applications for Dual Use (Orlando, FL, 1995).
34. M. G. Amin, P. J. Davis, and F. Allen, Jr., "An Application of the LMS Algorithm in Smoothing Pseudo Wigner Distribution," IEEE Trans. Signal Process., vol. 41, pp. 930-934 (1993).
35. V. C. Georgopoulos and D. Preis, "A Nonnegative Approximate Wigner Distribution with Accurate Low-Order Moments," in Proc. 13th Int. Conf. on Digital Signal Pocessing, DSP'97 (Santorini, Greece, 1997 July 1-4).
36. D. Preis and V. C. Georgopoulos, "Moment-Enhanced Spectrograms for Audio Signal Analysis," presented at the 106th Convention of the Audio Engineering Society, J. Audio Eng. Soc. (Abstracts), vol. 47, p. 534 (1999 June), preprint 4972.
37. B. Widrow and J. M. E. Hoff, "Adaptive Switching Circuits," in IRE WESCON Convention Rec. (1960), pp. 96-104.
38. V. C. Georgopoulos, "A Time-Frequency Representational Basis for Perceptual Systems with Applications to Neural Networks," Ph.D. dissertation, Tufts University, Medford, MA (1992).