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Abstract

Linear prediction modelling is used in a diverse area of applications such as data forecasting, speech recognition, low bit rate coding, model-based spectral analysis, interpolation, signal restoration etc. In statistical literature, linear prediction models are referred to as autoregressive (AR) processes. In this chapter we introduce the theory of linear prediction, and consider efficient methods for computation of the predictor coefficients. We study the forward, the backward and the lattice predictors, and consider various methods of formulation of the least squared error predictor coefficients. For the modelling of signals with a quasi-periodic structure, such as voiced speech, an extended linear predictor, that simultaneously utilises both the short and the long term correlation structures, is introduced. Finally the application of linear prediction in enhancement of noisy speech is considered. Further applications of linear prediction models, in this book, are in Chapter 11 on the interpolation of a sequence of lost samples, and in Chapters 12 and 13 on the detection and removal of impulsive noise and transient noise pulses.

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Bibliography

  1. Akaike H.(1970), Statistical Predictor Identification, Annals of the Institute of Statistical Mathematics, Vol. 22, Pages 203–217.MathSciNetzbMATHCrossRefGoogle Scholar
  2. Akaike H. (1974), A New Look at Statistical Model Identification, IEEE Trans. on Automatic Control, Vol. AC-19, Pages 716–723, Dec.MathSciNetCrossRefGoogle Scholar
  3. Anderson O.D. (1976), Time Series Analysis and Forecasting, The Box-Jenkins Approach, Butterworth, London.Google Scholar
  4. Ayre A.J. (1972), Probability and Evidence Columbia University Press.Google Scholar
  5. Box G.E.P, Jenkins G.M. (1976), Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco, California.zbMATHGoogle Scholar
  6. Burg J.P., (1975) Maximum Entropy Spectral Analysis, P.h.D. thesis, Stanford University, Stanford, California.Google Scholar
  7. Durbin J. (1959), Efficient Estimation of Parameters in Moving Average Models, Biometrica, Vol. 46, Pages 306–317.MathSciNetzbMATHGoogle Scholar
  8. Durbin J.(1960), “The Fitting of Time Series Models”, Rev. Int. Stat. Inst., Vol. 28 Pages 233–244.zbMATHCrossRefGoogle Scholar
  9. Fuller W.A. (1976), Introduction to Statistical Time Series, Wiley, New York.zbMATHGoogle Scholar
  10. Hansen J. H., Clements M. A. (1987). “Iterative Speech Enhancement with Spectral Constrains”, IEEE Proc. Int. Conf. on Acoustics, Speech and Signal Processing ICASSP-87, Vol. 1, Pages 189–192, Dallas, April.CrossRefGoogle Scholar
  11. Hansen J. H., Clements M. A. (1988). “Constrained Iterative Speech Enhancement with Application to Automatic Speech Recognition”, IEEE Proc. Int. Conf. on Acoustics, Speech and Signal Processing, ICASSP-88, Vol. 1, Pages 561–564, New York, April.Google Scholar
  12. Kobatake H., Inari J., Kakuta S. (1978), “Linear prediction Coding of Speech Signals in a High Ambient Noise Environment”, IEEE Proc. Int. Conf. on Acoustics, Speech and Signal Processing, Pages 472–475, April.Google Scholar
  13. Levinson N.(1947), “The Wiener RMS (Root Mean Square) Error Criterion in Filter Design and Prediction”, J. Math Phys., Vol. 25, Pages 261–278.MathSciNetGoogle Scholar
  14. Lim J. S., Oppenheim A. V. (1978), “All-Pole Modelling of Degraded Speech”, IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-26, No 3, pages 197–210, June.CrossRefGoogle Scholar
  15. Lim J. S., Oppenheim A. V. (1979), “Enhancement and Bandwidth Compression of Noisy Speech”, Proc. IEEE, No 67 Pages 1586–1604.CrossRefGoogle Scholar
  16. Makoul J.(1975), Linear Prediction: A Tutorial review. Proceedings of the IEEE Vol. 63, Pages 561–580.CrossRefGoogle Scholar
  17. Markel J.D., Gray A.H. (1976), Linear Prediction of Speech, Springer Verlag, New York.zbMATHCrossRefGoogle Scholar
  18. Rabiner L.R., Schafer R.W. (1976), Digital Processing of Speech Signals Prentice-Hall, Englewood Cliffs, N.J.Google Scholar
  19. Tong H. (1975), “Autoregressive Model Fitting with Noisy Data by Akaike’s Information Criterion”, IEEE Trans. Information Theory, Vol. IT-23, Pages 409–410.Google Scholar
  20. Stockham T.G, Cannon T.M, Ingebretsen R.B (1975), “Blind Deconvolution Through Digital Signal Processing”, IEEE Proc. Vol. 63, No. 4, Pages 678–692.CrossRefGoogle Scholar

Copyright information

© John Wiley & Sons Ltd. and B.G. Teubner 1996

Authors and Affiliations

  • Saeed V. Vaseghi
    • 1
  1. 1.Queen’s UniversityBelfastUK

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