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Abstrakty
We study estimation of theWigner time-frequency spectrum of Gaussian stochastic processes. Assuming the covariance belongs to the Feichtinger algebra, we construct an estimation kernel that gives a mean square error arbitrarily close to the infimum over kernels in the Feichtinger algebra.
Czasopismo
Rocznik
Tom
Strony
369--381
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Turin (TO), Italy
Bibliografia
- [1] H. G. Feichtinger, On a new Segal algebra, Monatsh. Math. 92 (1981), pp. 269-289.
- [2] H. G. Feichtinger, Modulation spaces on locally compact abelian groups, Technical Report, University of Vienna, 1983; also in: Wavelets and Their Applications, M. Krishna, R. Radha and S. Thangavelu (Eds.), Allied Publishers Private Limited, New Dehli Mumbai Kolkata Chennai Hagpur Ahmedabad Bangalore Hyderbad Lucknow, 2003, pp. 99-140.
- [3] H. G. Feichtinger and G. Zimmermann, A Banach space of test functions for Gabor analysis, in: Gabor Analysis and Algorithms - Theory and Applications, H. G. Feichtinger and T. Strohmer (Eds.), Birkhäuser, 1998, pp. 123-170.
- [4] P. Flandrin, Time-frequency/Time-scale Analysis, Academic Press, 1999.
- [5] G. B. Folland, Harmonic Analysis in Phase Space, Princeton University Press, 1989.
- [6] T. L. Grettenberg, A representation theorem for complex normal processes, IEEE Trans. Inform. Theory 11 (1965), pp. 305-306.
- [7] K. Gröchenig, Foundations of Time-Frequency Analysis, Birkhäuser, 2001.
- [8] C. W. Helstrom, Probability and Stochastic Processes for Engineers, Maxwell Macmillan, 1991.
- [9] M. Loève, Probability Theory, 2nd edition, Van Nostrand, 1963.
- [10] W. Martin, Time-frequency analysis of random signals, Proc. ICASSP-82 (1982), pp. 1325-1328.
- [11] W. Martin and P. Flandrin, Wigner-Ville spectral analysis of non-stationary processes, IEEE Trans. ASSP 33 (1985), pp. 1461-1470.
- [12] K. S. Miller, Complex Stochastic Processes, Addison-Wesley, 1974.
- [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics I, Wiley, 1975.
- [14] W. Rudin, Real and Complex Analysis, 3rd edition, McGraw-Hill, 1987.
- [15] A. M. Sayeed and D. L. Jones, Optimal kernels for nonstationary spectral estimation, IEEE Trans. Signal Process. 43 (1995), pp. 478-491.
- [16] G. F. Simmons, Topology and Modern Analysis, McGraw-Hill, 1963.
- [17] P. Wahlberg, The random Wigner distribution of Gaussian stochastic processes with covariance in S0(R2d), J. Funct. Spaces Appl. 3 (2) (2005), pp. 163-181.
Typ dokumentu
Bibliografia
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