Vector time-frequency AR models for nonstationary multivariate random processes

IEEE Transactions on Signal Processing

Volumn 57, Issue 12, 2009, Pages 4646-4659

  Jachan, Michael ^a   Matz, Gerald ^b   Hlawatsch, Franz ^b  

^a 82205 Gilching   (Germany)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Nonstationary multivariate random processes; Nonstationary spectral estimation; Order estimation; Parametric modeling; Time frequency analysis; Time varying AR models; Time varying systems; Vector processes; Yule Walker equations

Indexed keywords

AR MODELS; NONSTATIONARY; ORDER ESTIMATION; PARAMETRIC MODELING; SPECTRAL ESTIMATION; TIME FREQUENCY ANALYSIS; YULE-WALKER EQUATIONS;

BANDWIDTH; ESTIMATION; MULTIVARIANT ANALYSIS; RANDOM PROCESSES; SIMULATORS; SPECTRUM ANALYSIS; SPECTRUM ANALYZERS; TIME VARYING SYSTEMS; VECTORS;

FREQUENCY ESTIMATION;

EID: 70450270684     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2009.2026600     Document Type: Article

References (35)

1. P. Stoica and R. Moses, Introduction to Spectral Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1997.
2. S. M. Kay, Modern Spectral Estimation. Englewood Cliffs, NJ: Prentice- Hall, 1988.
3. M. Jachan and G. Matz, "Nonstationary vector AR modeling of wireless channels," in Proc. IEEE SPAWC, New York, Jun. 2005, pp. 648-652.
4. W. Hesse, E. Möller, M. Arnold, and B. Schack, "The use of timevariant EEG Granger causality for inspecting directed interdependencies of neural assemblies," J. Neurosci. Methods, vol.124, pp. 27-44, 2003.
5. E. A. Robinson and S. Treitel, Geophysical Signal Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1980.
6. M. Jachan, G. Matz, and F. Hlawatsch, "Time-frequency ARMA models and parameter estimators for underspread nonstationary random processes," IEEE Trans. Signal Process., vol.55, no.9, pp. 4366-4381, Sep. 2007.
7. M.Wax and T. Kailath, "Efficient inversion of Toeplitz-block Toeplitz matrix," IEEE Trans. Acoust., Speech, Signal Process., vol.31, pp. 1218-1221, Oct. 1983. (Pubitemid 14490802)
8. E. J. Hannan and M. Deistler, The Statistical Theory of Linear Systems. New York: Wiley, 1988.
9. T. Subba Rao, "The fitting of non-stationary time-series models with time-dependent parameters," J. Roy. Stat. Soc. Ser. B, vol.32, no.2, pp. 312-322, 1970.
10. L. A. Liporace, "Linear estimation of nonstationary signals," J. Acoust. Soc. Amer., vol.58, pp. 1288-1295, Dec. 1975.
11. Y. Grenier, "Time-dependent ARMA modeling of nonstationary signals," IEEE Trans. Acoust., Speech, Signal Process., vol.31, pp. 899-911, Aug. 1983.
12. K. B. Eom, "Time-varying autoregressive modeling of high range resolution radar signatures for classification of noncooperative targets," IEEE Trans. Aerosp. Electron. Syst., vol.35, pp. 974-988, Jul. 1999.
13. M. Niedźwiecki, Identification of Time-Varying Processes. New York: Wiley, 2000.
14. G. Matz and F. Hlawatsch, "Nonstationary spectral analysis based on time-frequency operator symbols and underspread approximations," IEEE Trans. Inf. Theory, vol.52, pp. 1067-1086, Mar. 2006.
15. G. Matz and F. Hlawatsch, "Time-varying power spectra of nonstationary random processes," in Time-Frequency Signal Analysis and Processing: A Comprehensive Reference, B. Boashash, Ed. Oxford, U.K.: Elsevier, 2003, ch. 9.4, pp. 400-409.
16. W. Kozek, "On the underspread/overspread classification of nonstationary random processes," in Proc. Int. Conf. Ind. Appl. Math., K. Kirchgässner, O. Mahrenholtz, and R. Mennicken, Eds., Mathematical Research, 1996, vol.3, pp. 63-66.
17. G. Matz and F. Hlawatsch, "Time-frequency transfer function calculus (symbolic calculus) of linear time-varying systems (linear operators) based on a generalized underspread theory," J. Math. Phys. (Special Issue on Wavelet and Time-Frequency Analysis), vol.39, pp. 4041-4071, Aug. 1998.
18. K. Gröchenig and M. Leinert,"Wiener's lemma for twisted convolution and Gabor frames," J. Amer. Math. Soc., vol.17, no.1, pp. 1-18, 2004.
19. K. Gröchenig, private communication, 2009.
20. L. A. Zadeh, "Frequency analysis of variable networks," Proc. IRE, vol.76, pp. 291-299, Mar. 1950.
21. P. A. Bello, "Characterization of randomly time-variant linear channels," IEEE Trans. Commun. Syst., vol.11, pp. 360-393, 1963.
22. G. Matz, "A time-frequency calculus for time-varying systems and nonstationary processes with applications," Ph.D. dissertation, Vienna Univ. of Technol., Vienna, Austria, Nov. 2000.
23. M. Jachan, "Time-frequency autoregressive moving-average modeling," Ph.D. dissertation, Vienna Univ. of Technol., Vienna, Austria, Jul. 2006.
24. G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD: The Johns Hopkins Univ. Press, 1996.
25. G. Matz and F. Hlawatsch, "Wigner distributions (nearly) everywhere: Time-frequency analysis of signals, systems, random processes, signal spaces, and frames," Signal Process., vol.83, no.7, pp. 1355-1378, 2003.
26. P. L. Combettes, "The foundations of set theoretic estimation," Proc. IEEE, vol.81, pp. 181-208, Feb. 1993.
27. M. Jachan, G. Matz, and F. Hlawatsch, "TFARMA models: Order estimation and stabilization," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP), Philadelphia, PA,Mar. 2005, vol.IV, pp. 301-304.
28. H. Akaike, "A new look at the statistical model identification, " IEEE Trans. Autom. Control, vol.19, pp. 716-723, Dec. 1974.
29. J. Rissanen, "Modeling by shortest data description," Automatica, vol.6, pp. 465-471, 1978.
30. H. L.Van Trees, Optimum Array Processing. NewYork:Wiley, 2002.
31. London Bat Group. [Online]. Available: http://www.londonbats.org.uk
32. P. Flandrin, Time-Frequency/Time-Scale Analysis. San Diego, CA: Academic, 1999.
33. F. Hlawatsch and P. Flandrin, "The interference structure of theWigner distribution and related time-frequency signal representations," in The Wigner Distribution-Theory and Applications in Signal Processing, W. Mecklenbräuker and F. Hlawatsch, Eds. Amsterdam, The Netherlands: Elsevier, 1997, pp. 59-133.
34. H. Akaike, "Block Toeplitz matrix inversion," SIAM J. Appl. Math., vol.24, pp. 234-241, Mar. 1973.
35. L. L. Scharf, Statistical Signal Processing. Reading, MA: Addison- Wesley, 1991.