Radiophysics and Quantum Electronics

, Volume 35, Issue 9–10, pp 509–520 | Cite as

Generalized Levinson algorithm and universal lattice filters

  • D. I. Lekhovitskii


Levinson's well-known algorithm for finding the triangular factors of matrices that are inverses of Toeplitz matrices is extended to the case of correlation matrices of arbitrary structure. Universal lattice filters are synthesized on this basis that are suitable for use in various types of signal-processing systems.


Correlation Matrice Toeplitz Matrice Arbitrary Structure Universal Lattice Triangular Factor 
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Literature Cited

  1. 1.
    R. Nitzberg, IEEE Trans.,AES-16, No. 1 (1980).Google Scholar
  2. 2.
    V. I. Zaritskii, V. N. Kokin, D. I. Lekhovitskii, et al., Izv. Vyssh. Uchebn. Zaved., Radiofiz.,28, No. 7, 863 (1985).Google Scholar
  3. 3.
    E. I. Lifanov and V. A. Likharev, Radiotekhnika, No. 5, 53 (1983).Google Scholar
  4. 4.
    V. M. Koshevoi, Radioélektronika,25, No. 9, 71 (1982).Google Scholar
  5. 5.
    D. I. Lekhovitskii, V. I. Zaritskii, et al., Preprint REI AS SSSR No. 8610, Moscow (1987).Google Scholar
  6. 6.
    B. Freidlander, TIIER,70, No. 8, 54 (1982).Google Scholar
  7. 7.
    S. M. Kay and S. P. Marple, TIIÉR,69, No. 11, 5 (1981).Google Scholar
  8. 8.
    V. G. Repin and G. P. Tartakovskii, Statistical Synthesis withA Priori Uncertainty and Adaptation of Information Systems [in Russian], Sovet-skoe Radio, Moscow (1977).Google Scholar
  9. 9.
    Yu. I. Abramovich and V. G. Kachur, Radiotekh. Élektron.,32, No. 7, 1547 (1987).Google Scholar
  10. 10.
    J. P. Burg, in: Modern Spectrum Analysis, IEEE Press, New York (1978), p. 34.Google Scholar
  11. 11.
    J. P. Burg, in: Modern Spectrum Analysis, IEEE Press, New York (1978), p. 42.Google Scholar
  12. 12.
    V. B. Mosunov. Zarubezhn, Radioélektron., No. 5, 3 (1985).Google Scholar
  13. 13.
    N. Levinson, J. Math. Phys.,25, 261 (1947).Google Scholar
  14. 14.
    V. V. Voevodin and E. E. Tyrtyshnikov, Computational Processes with Toeplitz Matrices [in Russian], Nauka, Moscow (1987).Google Scholar
  15. 15.
    F. Delsarte, Proc. IEEE Int. Conf. Acoust., Speech, and Signal Proc., Paris (1982), p. 1717.Google Scholar
  16. 16.
    V. V. Voevodin, Computational Fundamentals of Linear Algebra [in Russian], Nauka, Moscow (1977).Google Scholar
  17. 17.
    J. Box and G. Jenkins, Analysis of Time Series [Russian translation], No. 1, Mir, Moscow (1974).Google Scholar
  18. 18.
    G. Jacovitti and G. Scarano, TIIER,75, No. 7, 106 (1987).Google Scholar
  19. 19.
    Ya. D. Shirman and V. N. Manzhos, Theory and Practice of Radar-Data Processing with Noise Backgroud [in Russian], Radio i Svyaz', Moscow (1984).Google Scholar
  20. 20.
    V. V. Voevodin and Yu. A. Kuznetsov, Matrices and Calculations [in Russian], Nauka, Moscow (1984).Google Scholar
  21. 21.
    K. C. Sharman and T. S. Durrani, Proc. IEEE Int. Conf. Acoust., Speech, and Signal Proc., Boston, Vol. 1, No. 4, New York (1983), p. 348.Google Scholar
  22. 22.
    S. S. Kuzin and D. I. Lekhovitskii, Radiotekhnika, No. 6, 33 (1989).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • D. I. Lekhovitskii

There are no affiliations available

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