A geometric interpretation of the Rihaczek time-frequency distribution for stochastic signals

IEEE International Symposium on Information Theory - Proceedings

Volumn 2005-January, Issue , 2005, Pages

  Schreier, Peter J ^a   Scharf, Louis L ^b   Hanssen, Alfred ^c  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b Engineering Research Center and Hydraulics Laboratory   (United States)

^c UNIVERSITY OF TROMSØ   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER SERIES; FREQUENCY ESTIMATION; INFORMATION THEORY; RANDOM PROCESSES; ROBUSTNESS (CONTROL SYSTEMS); TIME SERIES;

BILINEAR TIME FREQUENCY DISTRIBUTION; GEOMETRIC INTERPRETATION; INNER PRODUCT; RIHACZEK DISTRIBUTION; SPECTRAL REPRESENTATIONS; STOCHASTIC SIGNALS; TIME AND FREQUENCIES; TIME-FREQUENCY DISTRIBUTIONS;

STOCHASTIC SYSTEMS;

EID: 34249828281     PISSN: 21578095     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ISIT.2005.1523481     Document Type: Conference Paper

References (14)

1. A. W. Rihaczek, “Signal Energy Distribution in Time and Frequency,” IEEE Trans. Inform. Theory, vol. 14, pp. 369-374, 1968
2. L. Cohen, “Generalized phase-space distribution functions,” J. Math. Phys., vol. 7, no. 5, pp. 781 - 786, May 1966
3. M. M. Rao, “Harmonizable, Cramér, and Karhunen classes of processes,” Handbook of Statistics, E. J. Hannan, P. R. Krishnaiah, M. M. Rao (eds.), vol. 5, Ch. 10, pp. 279 - 310, 1985
4. P. Flandrin, Time-Frequency/Time-Scale Analysis, Academic Press, San Diego, CA, 1999
5. B. Picinbono, P. Bondon, “Second-order statistics of complex signals,” IEEE Trans. Signal Processing, vol. 45, no. 2, pp. 411 - 419, Feb. 1997
6. P. J. Schreier, L. L. Scharf, “Second-order analysis of improper complex random vectors and processes,” IEEE Trans. Signal Processing, vol. 51, no. 3, pp. 714 - 725, Mar. 2003
7. P. J. Schreier, L. L. Scharf, “Stochastic time-frequency analysis using the analytic signal: why the complementary distribution matters,” IEEE Trans. Signal Processing, vol. 51, no. 12, pp. 3071 - 3079, Dec. 2003
8. L. L. Scharf, B. Friedlander, P. Flandrin, A. Hanssen, “The Hilbert space geometry of the stochastic Rihaczek distribution,” Proc. 35th Asilomar Conf. Signals, Systems, Comput., Pacific Grove, CA, Nov. 2001
9. A. Hanssen, Y. Larsen, L. L. Scharf, “Complex time-frequency and dual frequency spectra of harmonizable processes,” in Proc. EUSIPCO, Vienna, Austria, 2004
10. L. L. Scharf, B. Friedlander, “Toeplitz and Hankel kernels for estimating time-varying spectra of discrete-time random processes,” IEEE Trans. Signal Processing, vol. 49, no. 1, pp. 179 - 189, Jan. 2001
11. L. L. Scharf, P. J. Schreier, A. Hanssen, “The Hilbert space geometry of the Rihaczek distribution for stochastic analytic signals,” IEEE Signal Processing Lett., vol. 12, no. 4, pp. 297 - 300, Apr. 2005
12. B. Picinbono, P. Chevalier, “Widely linear estimation with complex data,” IEEE Trans. Signal Processing, vol. 43, no. 8, pp. 2030 - 2033, Aug. 1995
13. T. A. Øigård, L. L. Scharf, A. Hanssen, “Multivariate-multidimensional Rihaczek spectra and associated canonical correlations,” in Proc. 2004 IEEE Sensor Array and Multichannel Signal Processing Workshop, Sitges, Barcelona, Spain, July 2004
14. A. Hanssen, L.L. Scharf, “A theory of polyspectra for nonstationary stochastic processes,” IEEE Trans. Signal Processing, vol. 51, no. 5, pp. 1243 - 1252, 2003