Delta Levinson and Schur-Type RLS Algorithms for Adaptive Signal Processing

IEEE Transactions on Signal Processing

Volumn 42, Issue 7, 1994, Pages 1629-1639

  Fan, Howar ^a   Liu, Xiaqi ^b  

^a UNIVERSITY OF CINCINNATI   (United States)

^b Adaptive Technology Inc ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADAPTIVE SYSTEMS; ALGORITHMS; COMPUTER SIMULATION; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATHEMATICAL TRANSFORMATIONS; RANDOM PROCESSES; SIGNAL FILTERING AND PREDICTION;

ADAPTIVE SIGNAL PROCESSING; DELTA LEVINSON ALGORITHMS; DELTA OPERATORS; SCHUR TYPE RECURSIVE LEAST SQUARES ALGORITHMS;

SIGNAL PROCESSING;

EID: 0028468054     PISSN: 1053587X     EISSN: 19410476     Source Type: Journal    
DOI: 10.1109/78.298271     Document Type: Article

References (31)

1. N. Kalouptsidis, G. Carayannis, D. Manolakis, and E. Koukoutsis, “Efficient recursive in order least squares FIR filtering and prediction,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-33, no. 10, pp. 1175–1187, Oct. 1985.
2. N. Kalouptsidis and S. Theodoridis, “Parallel implementation of efficient LS algorithms for filtering and prediction,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-36, no. 11, pp. 1465–1469, Nov. 1987.
3. S. Caraboyas, N. Kalouptsidis, and C. Caroubalos, “Highly parallel transversal batch and block adaptive multichannel LS algorithms and application to decision feedback equalizers,” IEEE Trans. Acoust. Speech Signal Processing, vol. 38, no. 9, pp. 1380–1396, Sept. 1989.
4. E. Karlsson, “A geometric perspective on the Schur algorithm,” in Proc. IEEE ASSP Workshop Spectrum Est. Modeling (Minneapolis, MN), Aug. 1988, pp. 289–292.
5. P. Strobach, “New forms of Levinson and Schur algorithms,” IEEE Signal Processing Mag., vol. 8, no. 1, pp. 12–36, Jan. 1991.
6. P. Strobach, “Recursive triangular array ladder algorithms,” IEEE Trans. Signal Processing, vol. 39, no. 1, pp. 122–136, Jan. 1991.
7. P. Strobach, Linear Prediction Theory: A Mathematical Basis for Adaptive Systems. New York: Springer-Verlag, 1990.
8. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns Hopkins Univ. Press, 1983.
9. H. Fan, “A structural view of asymptotic convergence speed of adaptive IIR filtering algorithms: Part I—Infinite precision implementation,” IEEE Trans. Signal Processing, vol. 41, no. 4, pp. 1493–1517, Apr. 1993.
10. R. Vijayan, H. V. Poor, J. B. Moore, and G. C. Goodwin, “A Levinson-type algorithm for modeling fast-sampled data,” IEEE Trans. Automat. Contr., vol. AC-36, no. 3, pp. 314–321, Mar. 1991.
11. R. Vijayan, “Difference-operator-based models in statistical signal processing,” Ph.D. dissertation, Univ. of Illinois, Urbana, IL, 1991.
12. H. V. Poor and R. Vijayan, “High-speed statistical signal processing: The Levinson and Schur problems,” in Proc. 1990 Bilkent Int. Conf. New Trends Comm. Contr. Signal Processing (Ankara, Turkey), July 1990, pp. 1526–1540.
13. G. C. Goodwin, R. H. Middleton and H. V. Poor, “High-speed digital signal processing and control,” Proc. IEEE, vol. 80, no. 2, pp. 240–259, Feb. 1992.
14. C. J. Zarowski, “A QR-type algorithm for fitting the delta AR model to autocorrelation windowed data,” IEEE Trans. on Signal Processing, vol. 41, no. 4, April 1993, pp. 1728–1730.
15. F. Jabbari, “Lattice filters for RLS estimation of a delta operator-based model,” IEEE Trans. Automat. Contr., vol. AC-36, no. 7, pp. 869–875, July 1991.
16. S. Haykin, Adaptive Filter Theory Englewood Cliffs, NJ: Prentice-Hall, 1991, 2nd ed.
17. S. M. Kay, Modern Spectral Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1988.
18. J. G. Proakis, C. M. Rader, F. Ling, and C. L. Nikias, Advanced Digital Signal Processing New York: McMillan, 1992.
19. B. Friedlander, “Lattice filters for adaptive processing,” Proc. IEEE, vol. 70, no. 9, pp. 829–867, Sept. 1982.
20. C. Gueguen, “An introduction to displacement ranks and related fast algorithms,” in Signal Processing, Volume II (J. Lacoume, T. S. Durrani, and R. Stora, Eds.) Amsterdam: Elsevier Sci. Pub. B.V., North-Holland, 1985.
21. M. Morf, “Ladder forms in estimation and system identification,” in Proc. 11th Asilomar Conf. Circ. Syst. Comp. (Pacific Grove, CA), Nov. 1977, pp. 424–429.
22. D. T. L. Lee, M. Morf, and B. Friedlander, “Recursive least squares ladder estimation algorithms,” IEEE Trans. Acoust. Speech Signal Processing, vol. ASSP-29, no. 3, pp. 627–641, June 1981.
23. S. Y. Kung, VLSI Array Processors. Englewood Cliffs, NJ: Prentice-Hall, 1988.
24. H. T. Kung and W. M. Gentleman, “Matrix triangularization by systolic arrays,” in Proc. SPIE Int. Soc. Opt. Eng., 1983, pp. 18–26, vol. 431.
25. J. McWhirter, “Recursive least-squares minimization using a systolic array,” Proc. SPIE Int. Soc. Opt. Eng., 1983, pp. 431–415.
26. X. Liu and H. Fan, “Schur type algorithms for spatial LS estimation with highly pipelined architectures,” IEEE Trans. Signal Processing, vol. 41, no. 10, Oct. 1993, pp. 3010-3023.
27. G. O. Glentis and N. Kalouptsidis, “Efficient order recursive algorithms for multichannel least squares filtering,” IEEE Trans. Signal Processing, vol. 40, no. 6, pp. 1354–1374, June 1992.
28. G. O. Glentis and N. Kalouptsidis, “Fast adaptive algorithms for multichannel filtering and system identification,” IEEE Trans. Signal Processing, vol. 40, no. 10, pp. 2433–2459, Oct. 1992.
29. S. H. Ardalan, “Floating-point error analysis of recursive least-squares and least-mean-squares adaptive filters,” IEEE Trans. Circ. Syst., vol. CAS-33, no. 12, pp. 1192–1208, Dec. 1986.
30. C. Samson and V. U. Reddy, “Fixed point error analysis of the normalized ladder algorithm,” IEEE Trans. Acoust Speech Signal Processing, vol. ASSP-31, no. 5, pp. 1177–1190, Oct. 1983.
31. X. Liu and H. Fan, “Unequal length multichannel δ b-Levinson and Schur type RLS algorithms,” submitted to IEEE Trans. Signal Processing, 1993.