Linear Predic 7. Linear Prediction

Linear prediction plays a fundamental role in all aspects of speech. Its use seems natural and obvious in this context since for a speech signal the value of its current sample can be well modeled as a linear combination of its past values. In this chapter, we attempt to present the most important ideas on linear prediction. We derive the principal results, widely recognized by speech experts, in a very intuitive way without sacrificing mathematical rigor.

[1]  B.S. Atal.  The history of linear prediction , 2006, IEEE Signal Processing Magazine.

[2]  P. Alku,et al.  On line spectral frequencies , 2003, IEEE Signal Processing Letters.

[3]  Carlo Magi,et al.  Properties of line spectrum pair polynomials: a review , 2006 .

[4]  J. Makhoul.  Spectral analysis of speech by linear prediction , 1973 .

[5]  Steven Kay,et al.  Some results in linear interpolation theory , 1983 .

[6]  Joseph Picone,et al.  Signal modeling techniques in speech recognition , 1993, Proc. IEEE.

[7]  Y. Genin,et al.  Multichannel singular predictor polynomials , 1988 .

[8]  Alberto Leon-Garcia,et al.  A fast algorithm for optimal linear interpolation , 1993, IEEE Trans. Signal Process..

[9]  Biing-Hwang Juang,et al.  Line spectrum pair (LSP) and speech data compression , 1984, ICASSP.

[10]  J.H. McClellan,et al.  A simple proof of stability for all-pole linear prediction models , 1979, Proceedings of the IEEE.

[11]  Schuyler Quackenbush,et al.  Objective measures of speech quality , 1995 .

[12]  Rajendra Kumar,et al.  A fast algorithm for solving a Toeplitz system of equations , 1983, IEEE Trans. Acoust. Speech Signal Process..

[13]  Jacob Benesty,et al.  New Insights into the RLS Algorithm , 2004, EURASIP J. Adv. Signal Process..

[14]  J. Cadzow,et al.  Spectral estimation: An overdetermined rational model equation approach , 1982, Proceedings of the IEEE.

[15]  J. Durbin.  EFFICIENT ESTIMATION OF PARAMETERS IN MOVING-AVERAGE MODELS , 1959 .

[16]  John A. Stuller,et al.  Linear interpolation lattice , 1991, IEEE Trans. Signal Process..

[17]  O. Strand.  Multichannel complex maximum entropy (autoregressive) spectral analysis , 1977 .

[18]  Ronald W. Schafer,et al.  Digital Processing of Speech Signals , 1978 .

[19]  Biing-Hwang Juang,et al.  Optimal quantization of LSP parameters , 1993, IEEE Trans. Speech Audio Process..

[20]  Maurice Bellanger,et al.  Adaptive digital filters and signal analysis , 1987 .

[21]  John E. Markel,et al.  Linear Prediction of Speech , 1976, Communication and Cybernetics.

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

[23]  Monson H. Hayes,et al.  Statistical Digital Signal Processing and Modeling , 1996 .

[24]  Thomas Kailath,et al.  A view of three decades of linear filtering theory , 1974, IEEE Trans. Inf. Theory.

[25]  E. Robinson,et al.  Recursive solution to the multichannel filtering problem , 1965 .

[26]  Paavo Alku,et al.  A time-domain interpretation for the LSP decomposition , 2004, IEEE Transactions on Speech and Audio Processing.

[27]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[28]  Philippe Delsarte,et al.  The split Levinson algorithm , 1986, IEEE Trans. Acoust. Speech Signal Process..

[29]  C. Therrien,et al.  On the relation between triangular matrix decomposition and linear prediction , 1983, Proceedings of the IEEE.

[30]  J. Makhoul,et al.  Linear prediction: A tutorial review , 1975, Proceedings of the IEEE.

[31]  Jingdong Chen,et al.  Acoustic MIMO Signal Processing , 2006 .

[32]  J. Makhoul.  Stable and efficient lattice methods for linear prediction , 1977 .

[33]  Bernard C. Picinbono,et al.  Some properties of prediction and interpolation errors , 1988, IEEE Trans. Acoust. Speech Signal Process..

[34]  S.M. Kay,et al.  Spectrum analysis—A modern perspective , 1981, Proceedings of the IEEE.

[35]  P. Whittle.  On the fitting of multivariate autoregressions, and the approximate canonical factorization of a spectral density matrix , 1963 .

[36]  James Durbin,et al.  The fitting of time series models , 1960 .

[37]  N. Levinson.  The Wiener (Root Mean Square) Error Criterion in Filter Design and Prediction , 1946 .

[38]  Jacob Benesty,et al.  Computation of the condition number of a nonsingular symmetric toeplitz matrix with the Levinson-durbin algorithm , 2006, IEEE Transactions on Signal Processing.

[39]  Soo Ngee Koh,et al.  Enhanced Itakura measure incorporating masking properties of human auditory system , 2003, Signal Process..