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Robust Parametric Modeling of Speech in Additive White Gaussian Noise

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DOI: 10.4236/jsip.2015.62010    4,620 Downloads   5,120 Views   Citations

ABSTRACT

In estimating the linear prediction coefficients for an autoregressive spectral model, the concept of using the Yule-Walker equations is often invoked. In case of additive white Gaussian noise (AWGN), a typical parameter compensation method involves using a minimal set of Yule-Walker equation evaluations and removing a noise variance estimate from the principal diagonal of the autocorrelation matrix. Due to a potential over-subtraction of the noise variance, however, this method may not retain the symmetric Toeplitz structure of the autocorrelation matrix and thereby may not guarantee a positive-definite matrix estimate. As a result, a significant decrease in estimation performance may occur. To counteract this problem, a parametric modelling of speech contaminated by AWGN, assuming that the noise variance can be estimated, is herein presented. It is shown that by combining a suitable noise variance estimator with an efficient iterative scheme, a significant improvement in modelling performance can be achieved. The noise variance is estimated from the least squares analysis of an overdetermined set of p lower-order Yule-Walker equations. Simulation results indicate that the proposed method provides better parameter estimates in comparison to the standard Least Mean Squares (LMS) technique which uses a minimal set of evaluations for determining the spectral parameters.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Trabelsi, A. , Mohamed, O. and Audet, Y. (2015) Robust Parametric Modeling of Speech in Additive White Gaussian Noise. Journal of Signal and Information Processing, 6, 99-108. doi: 10.4236/jsip.2015.62010.

References

[1] Proakis, J.G., Rader, C.M., Ling, F. and Nikias, C.L. (1992) Advanced Digital Signal Processing. Macmillan Publishing Company, New York.
[2] Pagano, M. (1974) Estimation of Models of Autoregressive Signal Plus White Noise. The Annals of Statistics, 2, 99-108. http://dx.doi.org/10.1214/aos/1176342616
[3] Chakhchoukh, Y. (2010) A New Robust Estimation Method for ARMA Models. IEEE Transactions on Signal Processing, 58, 3512-3522. http://dx.doi.org/10.1109/TSP.2010.2046413
[4] Kay, S.M. (1979) The Effects of Noise on the Autoregressive Spectral Estimator. IEEE Transactions on Acoustics, Speech and Signal Processing, 27, 478-485.
http://dx.doi.org/10.1109/TASSP.1979.1163275
[5] Dominguez, L.V. (1990) New Insights into the High-Order Yule-Walker Equations. IEEE Transactions on Acoustics, Speech and Signal Processing, 38, 1649-1651.
[6] Chan, Y.T. and Langford, R.P. (1982) Spectral Estimation via High-Order Yule-Walker Equations. IEEE Transactions on Acoustics, Speech and Signal Processing, 30, 689-698.
http://dx.doi.org/10.1109/TASSP.1982.1163946
[7] Jain, V.K. and Atal, B.S. (1985) Robust LPC Analysis of Speech by Extended Correlation Matching. IEEE International Conference on Acoustics, Speech and Signal Processing, 10, 473-476.
http://dx.doi.org/10.1109/ICASSP.1985.1168377
[8] Jachan, M., Matz, G. and Hlawatsch, F. (2007) Time-Frequency ARMA Models and Parameter Estimators for Underspread Nonstationary Random Processes. IEEE Transactions on Signal Processing, 55, 4366-4376.
[9] Cadzow, J.A. (1982) Spectral Estimation: An Overdetermined Rational Model Equation Approach. Proceedings of the IEEE, 70, 907-939. http://dx.doi.org/10.1109/PROC.1982.12424
[10] Izraelevitz, D. and Lim, J.S. (1985) Properties of the Overdetermined Normal Equation Method for Spectral Estimation When Applied to Sinusoids in Noise. IEEE Transactions on Acoustics, Speech and Signal Processing, 33, 406-412.http://dx.doi.org/10.1109/TASSP.1985.1164574
[11] Jackson, L.B., Jianguo, H., Richards, K. and Haiguang, C. (1989) AR, ARMA, and AR-in-Noise Modeling by Fitting Windowed Correlation Data. IEEE Transactions on Acoustics, Speech and Signal Processing, 37, 1608-1612.
[12] Kay, S.M. (1980) Noise Compensation for Autoregressive Spectral Estimates. IEEE Transactions on Acoustics, Speech and Signal Processing, 28, 292-303.
[13] Hu, H.T. (1998) Linear Prediction Analysis of Speech Signals in the Presence of White Gaussian Noise with Unknown Variance. IEE Proceedings on Vision, Image and Signal Processing, 145, 303-308.
http://dx.doi.org/10.1049/ip-vis:19982014
[14] Zhao, Q., Shimamura, T. and Suzuki, J. (2000) Improvement of LPC Analysis of Speech by Noise Compensation. Electronics and Communications in Japan, 83, 73-83.
[15] Trabelsi, A., Boyer, F.R., Savaria, Y. and Boukadoum, M. (2007) Iterative Noise-Compensated Method to Improve LPC Based Speech Analysis. IEEE International Conference on Electronics, Circuits and Systems, Marrakech, 11-14 December 2007, 1364-1367.
http://dx.doi.org/10.1109/ICECS.2007.4511252
[16] Fattah, S.A., Zhu, W.P. and Ahmad, M.O. (2011) Identification of Autoregressive Moving Average Systems Based on Noise Compensation in the Correlation Domain. IET Signal Processing, 5, 292-305.
http://dx.doi.org/10.1049/iet-spr.2009.0240
[17] Stewart, G.W. (1993) On the Early History of the Singular Value Decomposition. Journal of the Society for Industrial and Applied Mathematics, 35, 551-566. http://dx.doi.org/10.1137/1035134
[18] Tufts, D. and Kumaresan, R. (1982) Singular Value Decomposition and Improved Frequency Estimation Using Linear Prediction. IEEE Transactions on Acoustics, Speech and Signal Processing, 30, 671-675. http://dx.doi.org/10.1109/TASSP.1982.1163927
[19] Lee, S. and Hayes, M.H. (2004) Properties of the Singular Value Decomposition for Efficient Data Clustering. IEEE Signal Processing Letters, 11, 862-866. http://dx.doi.org/10.1109/LSP.2004.833513
[20] Golub, G.H. and Kahan, W.M. (1965) Calculating the Singular Values and Pseudo-Inverse of a Matrix. Journal of the Society for Industrial and Applied Mathematics, 2, 205-224.
http://dx.doi.org/10.1137/0702016
[21] Golub, G.H. and Reinsch, C. (1970) Singular Value Decomposition and Least Squares Solutions. Numerische Mathematik, 14, 403-420. http://dx.doi.org/10.1007/BF02163027
[22] James, D. and Kahan, W.M. (1990) Accurate Singular Values of Bidiagonal Matrices. SIAM Journal on Scientific and Statistical Computing, 11, 873-912. http://dx.doi.org/10.1137/0911052
[23] Gu, M. and Eisenstat, S.C. (1995) A Divide-and-Conquer Algorithm for the Bidiagonal SVD. SIAM Journal on Matrix Analysis and Applications, 16, 79-92.
http://dx.doi.org/10.1137/S0895479892242232
[24] Chan, T.F. (1982) An Improved Algorithm for Computing the Singular Value Decomposition. ACM Transaction on Mathematical Software, 8, 72-83. http://dx.doi.org/10.1145/355984.355990
[25] Tierney, J. (1980) A Study of LPC Analysis of Speech in Additive Noise. IEEE Transactions on Acoustics, Speech and Signal Processing, 28, 389-397.
http://dx.doi.org/10.1109/TASSP.1980.1163423
[26] Cadzow, J.A. (1980) High Performance Spectral Estimation—A New ARMA Method. IEEE Transactions on Acoustics, Speech and Signal Processing, 28, 524-529.
http://dx.doi.org/10.1109/TASSP.1980.1163440
[27] Paliwal, K.K. (1988) Estimation of Noise Variance from the Noisy AR Signal and Its Application in Speech Enhancement. IEEE Transactions on Acoustics, Speech and Signal Processing, 36, 292-294.
[28] Nilsson, M., Soli, S.D. and Sullivan, J.A. (1994) Development of the Hearing in Noise Test for the Measurement of Speech Reception Thresholds in Quit and in Noise. Journal of the Acoustical Society of America, 95, 1085-1099. http://dx.doi.org/10.1121/1.408469

  
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