A Tree-Structured Piecewise Linear Adaptive Filter

IEEE Transactions on Information Theory

Volumn 39, Issue 6, 1993, Pages 1907-1922

  Gelfand, Saul B ^a   Ravishankar, C S ^b  

^a PURDUE UNIVERSITY   (United States)

^b Voiceband Processing Department COMSAT Corporation ^*  (United States)

Author keywords

Adaptive filtering; convergence analysis; dependent data; echo cancellation; nonlinear filtering; order analysis; penalty methods; stochastic gradient algorithms; tree structured methods

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SIMULATION; ECHO CANCELLATION; ESTIMATION; HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; POLYNOMIALS; REGRESSION ANALYSIS; ROBUSTNESS (CONTROL SYSTEMS); TREES (MATHEMATICS);

CONVERGENCE ANALYSIS; DEPENDENT DATA; NONLINEAR ADAPTIVE FILTER; ORDER ANALYSIS; PENALTY METHODS; PIECEWISE LINEAR ADAPTIVE FILTER; STOCHASTIC GRADIENT ALGORITHMS; TRAINING ALGORITHM; TREE STRUCTURED METHOD;

SIGNAL FILTERING AND PREDICTION;

EID: 0027696001     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.265499     Document Type: Article

References (23)

1. V. J. Mathews, “Adaptive polynomial filters,” IEEE Signal Processing Mag., pp. 10–26, July 1991.
2. M. Schetzen, Volterra and Wiener Theories of Nonlinear Systems. New York: Wiley, 1980.
3. G. J. Gibson, S. Siu, and C. F. N. Cowan, “The application of nonlinear structures to the reconstruction of binary signals,” IEEE Trans. Signal Processing, vol. 39, pp. 1877–1884, Aug. 1991.
4. O. Agazzi, D. G. Messerschmitt, and D. A. Hodges, “Nonlinear echo cancellation of data signals,” IEEE Trans. Commun., vol. COM-30, pp. 2421–2433, Nov. 1982.
5. M. M. Sondhi and D. A. Berkley, “Silencing echoes on the telephone network,” Proc. IEEE, vol. 68, pp. 948–963, Aug. 1980.
6. E. J. Thomas, “An adaptive echo canceler in a nonideal environment (nonlinear or time variant),” Bell Syst. Tech. I., vol. 50, pp. 2779–2795, 1971.
7. J. G. Proakis, Digital Communications. New York: McGraw-Hill, 1983.
8. N. S. Jayant and P. S. Noll, Digital Coding of Waveforms: Principles and Applications to Speech and Video. Englewood Cliffs, NJ: Prentice-Hall, 1984.
9. H. Tong, Threshold Models in Nonlinear Time Series Analysis, vol. 21 of Lecture Notes in Statistics. Berlin: Springer, 1983.
10. M. B. Priestly, Spectral Analysis and Time Series, Vol. 2. New York: Academic, 1981.
11. L. Brieman, J. H. Friedman, R. A. Olshen, and C. J. Stone, Classification and Regression Trees. Wadsworth Int., 1984.
12. S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, “An iterative growing and pruning algorithm for classification tree design,” IEEE Trans. Pattern Anal. Machine Intell., vol. 13, pp. 163–174, Feb. 1991.
13. P. A. Chou, T. Lookabaugh, and R. M. Gray, “Optimal pruning with applications to tree structured source coding and modeling,” IEEE Trans. Inform. Theory, vol. IT-35, pp. 299–315, Mar. 1985.
14. R. M. Goodman and P. Smyth, “Decision tree from a communication theory standpoint,” IEEE Trans. Inform. Theory, vol. IT-34, pp. 979–993, Nov. 1988.
15. J. K. Kim and L. D. Davisson, “Adaptive linear estimation for stationary MD-ependent processes,” IEEE Trans. Inform. Theory, vol. IT-21, pp. 23–31, Jan. 1975.
16. D. Farden, J. Goding, Jr., and K. Sayood, “On the ‘desired behavior’ of adaptive signal processing algorithms,” in Proc. 1979 Int. Conf. Acoust., Speech, Signal Processing, pp. 941–944, Apr. 1979.
17. S. K. Jones, R. K. Cavin, and W. M. Reed, “Analysis of error-gradient adaptive linear estimator for a class of stationary dependent processes,” IEEE Trans. Inform. Theory, vol. IT-28, pp. 318–329, Mar. 1982.
18. O. Macchi and E. Eweda, “Second order convergence analysis of stochastic adaptive linear filtering,” IEEE Trans. Automat. Contr., vol. AC-28, pp. 76–85, Jan. 1983.
19. A. Krieger and E. Masry, “Convergence analysis of adaptive linear estimation for stationary dependent processes,” IEEE Trans. Inform. Theory, vol. IT-34, pp. 642–654, July 1988.
20. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, NJ: Prentice-Hall, 1986.
21. O. Macchi, “Resolution adaptative de l'equation de Wiener Hopf,” Ann. Inst. Henri Poincare, vol. 14, pp. 357–379, 1978.
22. J. Bellamy, Digital Telephony. New York: Wiley, 1982.
23. S. B. Gelfand, C. S. Ravishankar, and E. J. Delp, “Tree-structured piecewise linear adaptive equalization,” IEEE Trans. Commun., vol. 41, pp. 70–82, Jan. 1993.