The theory of linear prediction

Synthesis Lectures on Signal Processing

Volumn 3, Issue , 2007, Pages 1-181

  Vaidyanathan, P P ^a  

^a CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Autoregressive models; Filtering; Lattice structures; Levinson's recursion; Line spectral processes; Linear estimation; Linear prediction theory; Smoothing; Vector linear prediction

Indexed keywords

AUTOREGRESSIVE MODELS; LATTICE STRUCTURES; LINE SPECTRAL PROCESSES; LINEAR ESTIMATION; LINEAR PREDICTION THEORY; VECTOR LINEAR PREDICTION;

COMPUTATIONAL METHODS; MATHEMATICAL MODELS; SIGNAL FILTERING AND PREDICTION; STATISTICAL METHODS; VECTORS;

DIGITAL SIGNAL PROCESSING;

EID: 37749043733     PISSN: 19321236     EISSN: 19321694     Source Type: Book Series    
DOI: 10.2200/S00086ED1V01Y200712SPR03     Document Type: Article

References (85)

1. Anderson, B. D. O., and Moore, J. B. Optimal filtering, Prentice-Hall, Englewood Cliffs, NJ, 1979.
2. Antoniou, A. Digital signal processing: signals, systems, and filters, McGraw-Hill, New York, 2006.
3. Antoniou, A., and Lu, W.-S. Practical optimization; algorithms and engineering applications, Springer, New York, 2007.
4. Atal, B. S., and Schroeder, M. R. "Adaptive predictive coding of speech signals," Bell. Sys. Teco. J., vol. 49, pp. 1973-1986, October 1970. doi:10.1109/ICASSP.1980.1170967
5. Atal, B. S., and Schroeder, M. R. "Predictive coding of speech signals and subjective error criteria," IEEE Trans. Acoust. Speech Signal Process., vol. 27, pp. 247-254, June 1979.
6. Balabanian, N., and Bickart, T. A. Electrical network theory, John Wiley & Sons, New York, 1969.
7. Bellman, R. Introduction to matrix analysis, McGraw-Hill, New York, 1960.
8. Berlekamp, E. R. Algebraic coding theory, McGraw-Hill, New York, 1969.
9. Blahut, R. E. Fast algorithms for digital signal processing, Addison-Wesley, Reading, MA, 1985.
10. Burg, J. P. "The relationship between maximum entropy spectra and maximum likelihood spectra," Geophysics, vol. 37, pp. 375-376, April 1972. doi:10.1190/1.1440265
11. Chandrasekhar, S. "On the radiative equilibrium of a stellar atmosphere," Astrophys. J., vol. 106, pp. 152-216, 1947.
12. Chellappa, R., and Kashyap, R. L. "Texture synthesis using 2-D noncausal autoregressive models," IEEE Trans. Acoust. Speech Signal Process., vol. 33, pp. 194-203, February 1985.
13. Chong, E. K. P., and Zak, S. H. An introduction to optimization, John Wiley & Sons, New York, 2001. doi:10.1109/MAP.1996.500234
14. Churchill, R. V., and Brown, J. W. Introduction to complex variables and applications, McGrawHill, New York, 1984.
15. Cover, T. M., and Thomas, J. A. Elements of information theory, John Wiley & Sons, New York, 1991.
16. Deller, J. R., Proakis, J. G., and Hansen, J. H. L. Discrete-time processing of speech signals, Macmillan, New York, 1993.
17. Friedlander, B. "A lattice algorithm for factoring the spectrum of a moving average process," IEEE Trans. Automat. Control, vol. 28, pp. 1051-1055, November 1983. doi:10.1109/TAC.1983.1103175
18. Gersho, A., and Gray, R. M. Vector quantization and signal compression, Kluwer Academic Press, Boston, 1992.
19. Golub, G. H., and Van Loan, C. F. Matrix computations, Johns Hopkins University Press, Baltimore, MD, 1989.
20. Gorokhov, A., and Loubaton, P. "Blind identification of MIMO-FIR systems: a generalized linear prediction approach," Signal Process., vol. 73, pp. 105-124, 1999. doi:10.1016/S0165-1684(98)00187-X
21. Gray, Jr., A. H. "Passive cascaded lattice digital filters," IEEE Trans. Circuits Syst., vol. CAS-27, pp. 337-344, May 1980.
22. Gray, R. M. "On asymptotic eigenvalue distribution of Toeplitz matrices," IEEE Trans. Inform. Theory, vol. 18, pp. 725-730, November 1972.
23. Gray, Jr., A. H., and Markel, J. D. "Digital lattice and ladder filter synthesis," IEEE Trans. Audio Electroacoust. vol. AU-21, pp. 491-500, December 1973. doi:10.1109/TAU.1973.1162522
24. Gray, Jr., A. H., and Markel, J. D. "A normalized digital filter structure," IEEE Trans. Acoust. Speech Signal Process., vol. ASSP-23, pp. 268-277, June 1975. doi:10.1109/TASSP.1975.1162680
25. Grenander, U., and Szego, G. Toeplitz forms and their applications, University of California Press, Berkeley, CA, 1958.
26. Hayes, M. H. Statistical digital signal processing and modeling, John Wiley & Sons, New York, 1996.
27. Haykin, S. Adaptive filter theory, Prentice-Hall, Upper Saddle River, NJ, 1986 and 2002.
28. Horn R. A., and Johnson, C. R. Matrix analysis, Cambridge University Press, Cambridge, 1985.
29. Itakura, F. "Line spectrum representation of linear predictive coefficients of speech signals," J. Acoust. Soc. Am., vol. 57, 1975.
30. Itakura, F., and Saito, S. "A statistical method for estimation of speech spectral density and formant frequencies," Trans IECE Jpn., vol. 53-A, pp. 36-43, 1970.
31. Jayant, N. S., and Noll, P. Digital coding of waveforms, Prentice-Hall, Englewood Cliffs, NJ, 1984. doi:10.1016/0165-1684(85)90053-2
32. Kailath, T. "A view of three decades of linear filtering theory," IEEE Trans. Inform. Theory, vol. 20, pp. 146-181, March 1974. doi:10.1109/TIT.1974.1055174
33. Kailath, T. Linear systems, Prentice Hall, Inc., Englewood Cliffs, NJ, 1980.
34. Kailath, T., Kung S-Y., and Morf, M. "Displacement ranks of a matrix," Am. Math. Soc., vol. 1, pp. 769-773, September 1979. doi:10.1016/0022-247X(79)90124-0
35. Kailath, T., Sayed, A. H., and Hassibi, B. Linear estimation, Prentice-Hall, Englewood Cliffs, NJ, 2000.
36. Kang, G. S., and Fransen, L. J. "Application of line-spectrum pairs to low-bit-rate speech coders," Proc. IEEE Int. Confi Acoust. Speech Signal Process., pp. 7.3.1-7.3.4, May 1995.
37. Kay, S. M., and Marple, S. L., Jr., "Spectrum analysis - a modern perspective," Proc. IEEE, vol. 69, pp. 1380-1419, November 1981.
38. Kay, S. M. Modern spectral estimation: theory and application, Prentice-Hall, Englewood Cliffs, NJ, 1988.
39. Kolmogorov, A. N. "Interpolation and extrapolation of stationary random sequences," Izv. Akad. Nauk SSSR Ser. Mat. 5, pp. 3-14, 1941.
40. Kreyszig, E. Advanced engineering mathematics, John Wiley & Sons, New York, 1972.
41. Kumaresan, R., and Tufts, D. W. "Estimating the angles of arrival of multiple plane waves," IEEE Trans. Aerosp. Electron. Syst., vol. 19, pp. 134-139, January 1983.
42. Lang, S. W., and McClellan, J. H. "A simple proof of stability for all-pole linear prediction models," Proc. IEEE, vol. 67, pp. 860-861, May 1979.
43. Lepschy, A., Mian, G. A., and Viaro, U. "A note on line spectral frequencies," IEEE Trans. Acoust. Speech Signal Process., vol. 36, pp. 1355-1357, August 1988. doi:10.1109/29.1664
44. Levinson, N. "The Wiener rms error criterion in filter design and prediction," J. Math. Phys., vol. 25, pp. 261-278, January 1947.
45. Lopez-Valcarce, R., and Dasgupta, S. "Blind channel equalization with colored sources based on second-order statistics: a linear prediction approach," IEEE Trans. Signal Process., vol. 49, pp. 2050-2059, September 2001. doi:10.1109/78.942633
46. Makhoul, J. "Linear prediction: a tutorial review," Proc. IEEE, vol. 63, pp. 561-580, April 1975.
47. Makhoul, J. "Stable and efficient lattice methods for linear prediction," IEEE Trans. Acoust. Speech Signal Process., vol. 25, pp. 423-428, October 1977.
48. Makhoul, J., Roucos, S., and Gish, H. "Vector quantization in speech coding," Proc. IEEE, vol. 73, pp. 1551-1588, November 1985. doi:10.1109/ISCAS.2003.1206020
49. Manolakis, D. G., Ingle, V. K., and Kogon, S. M. Statistical and adaptive signal processing, McGraw-Hill, New York, 2000.
50. Markel, J. D., and Gray, A. H., Jr. Linear prediction of speech, Springer-Verlag, New York, 1976.
51. Marple, S. L., Jr. Digital spectral analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987. doi:10.1121/1.398548
52. Mitra, S. K. Digital signal processing: a computer-based approach, McGraw-Hill, New York, 2001.
53. Moon, T. K., and Stirling, W. C. Mathematical methods and algorithms for signal processing, Prentice-Hall, Upper Saddle River, NJ, 2000.
54. Oppenheim, A. V., and Schafer, R. W. Discrete-time signal processing, Prentice-Hall, Englewood Cliffs, NJ, 1999.
55. Papoulis, A. Probability, random variables and stochastic processes, McGraw-Hill, New York, 1965.
56. Papoulis, A. "Maximum entropy and spectrum estimation: a review," IEEE Trans. Acoust. Speech Signal Process., vol. 29, pp. 1176-1186, December 1981.
57. Paulraj, A., Roy, R., and Kailath, T. "A subspace rotation approach to signal parameter estimation," Proc. IEEE, vol. 74, pp. 1044-1046, July 1986.
58. Peebles, Jr., P. Z. Probability, random variables and random signal principles, McGraw-Hill, New York, 1987.
59. Pisarenko, V. F. "The retrieval of harmonics from a covariance function," Geophys. J. R. Astron. Soc., vol. 33, pp. 347-366, 1973. doi:10.1111/j.1365-246X.1973.tb03424.x
60. Proakis, J. G., and Manolakis, D. G. Digital signal processing: principles, alogrithms and applications, Prentice-Hall, Upper Saddle River, NJ, 1996.
61. Rabiner, L. R., and Schafer, R. W. Digital processing of speech signals, Prentice-Hall, Englewood Cliffs, NJ, 1978.
62. Rao, S. K., and Kailath, T. "Orthogonal digital lattice filters for VLSI implementation," IEEE Trans. Circuits Syst., vol. CAS-31, pp. 933-945, November 1984.
63. Robinson, E. A. "A historical perspective of spectrum estimation," Proc. IEEE, vol. 70, pp. 885-907, September 1982.
64. Roy, R., and Kailath, T. "ESPRIT - estimation of signal parameters via rotational invariance techniques," IEEE Trans. Acoust. Speech Signal Process., vol. 37, pp. 984-995, July 1989. doi:10.1109/29.32276
65. Rudin, W. Real and complex analysis, McGraw-Hill, New York, 1974.
66. Satorius, E. H., and Alexander S. T. "Channel equalization using adaptive lattice algorithms," IEEE Trans. Commun., vol. 27, pp. 899-905, June 1979. doi:10.1109/TCOM.1979.1094477
67. Sayed, A. H. Fundamentals of adaptive filtering, IEEE Press, John Wiley & Sons, Hoboken, NJ, 2003.
68. Schmidt, R. O. "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propagation, vol. 34, pp. 276-280, March 1986 (reprinted from the Proceedings of the RADC Spectrum Estimation Workshop, 1979). doi:10.1109/TAP.1986.1143830
69. Schroeder, M. Computer speech: recognition, compression and synthesis, Springer-Verlag, Berlin, 1999.
70. Soong, F. K., and Juang B.-H, "Line spectrum pair (LSP) and speech data compression," Proc. IEEE Int. Conf. Acoust. Speech Signal Process., pp. 1.10.1-1.10.4, March 1984.
71. Soong, F. K., and Juang B.-H, "Optimal quantization of LSP parameters," IEEE Trans. Speech Audio Process., vol. 1, pp. 15-24, January 1993.
72. Strobach, P. Linear prediction theory, Springer-Verlag, Berlin, 1990.
73. Therrien, C. W. Discrete random signals and statistical signal processing, Prentice-Hall, Upper Saddle River, NJ, 1992.
74. Vaidyanathan, P. P. "The discrete-time bounded-real lemma in digital filtering," IEEE. Trans. Circuits Syst., vol. CAS-32, pp. 918-924, September 1985. doi:10.1109/TCS.1985.1085815
75. Vaidyanathan, P. P. "Passive cascaded lattice structures for low sensitivity FIR filter design, with applications to filter banks," IEEE Trans. Circuits Syst., vol. CAS-33, pp. 1045-1064, November 1986. doi:10.1109/TCS.1986.1085867
76. Vaidyanathan, P. P. "On predicting a band-limited signal based on past sample values," Proc. IEEE, vol. 75, pp. 1125-1127, August 1987.
77. Vaidyanathan, P. P. Multirate systems and filter banks, Prentice-Hall, Englewood Cliffs, NJ, 1993. doi:10.1109/78.382395
78. Vaidyanathan, P. P., and Mitra, S. K. "Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures," Proc. IEEE, vol. 72, pp. 404-423, April 1984.
79. Vaidyanathan, P. P., and Mitra, S. K. "A general family of multivariable digital lattice filters," IEEE. Trans. Circuits Syst., vol. CAS-32, pp. 1234-1245, December 1985. doi:10.1109/TCS.1985.1085661
80. Vaidyanathan, P. P., Mitra, S. K., and Neuvo, Y. "A new approach to the realization of low sensitivity IIR digital filters," IEEE Trans. Acoust. Speech Signal Process., vol. ASSP-34, pp. 350-361, April 1986. doi:10.1109/TASSP.1986.1164829
81. Vaidyanathan, P. P., Tuqan, J., and Kirac, A. "On the minimum phase property of prediction-error polynomials," IEEE Signal Process. Lett., vol. 4, pp. 126-127, May 1997. doi:10.1109/97.575554
82. Van Trees, H. L. Optimum array processing, John Wiley & Sons, New York, 2002.
83. Wainstein, L. A., and Zubakov, V. D. Extraction of signals from noise, Prentice-Hall, London, 1962. doi:10.1119/1.1969250
84. Weiner, N. Extrapolation, interpolation and smoothing of stationary time series, John Wiley & Sons, New York, 1949.
85. Weiner, N., and Masani, P. "The prediction theory of multivariate stochastic processes," Acta Math., part 1: vol. 98, pp. 111-150, 1957; part 2: vol. 99, pp. 93-137, 1958.