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Linear and Dynamic System Model

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Advances in Non-Linear Modeling for Speech Processing

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Abstract

In this chapter, we have discussed two types of widely used mathematical models, the linear model and the dynamic system model. The linear model and the dynamic system model (often formulated in a specific form called the state-space model) are two distinct types of mathematical structures, both with popular applications in many disciplines of engineering. These two types of the models have very different mathematical properties and computational structures. Instead of using a high-dimensional linear model to represent the temporal correlation structure of a signal, a low-dimensional dynamic system model can be used for efficient computations.

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References

  1. Rabiner LR, Juang BH (1993) Fundamentals of speech recognition. Prentice-Hall of India, New Delhi

    Google Scholar 

  2. Hansen J, Proakis J (2000) Discrete-time processing of speech signals, 2nd edn. IEEE Press, New York

    Google Scholar 

  3. Mammone R, Zhang X, Ramachandran R (1996) Robust speaker recognition: a feature based approach. IEEE Signal Process Mag 13:58–71

    Article  Google Scholar 

  4. Gudnason J (2007) Voice source cepstrum processing for speaker identification. Ph.D. thesis, University of London

    Google Scholar 

  5. Dunn HK (1961) Methods of measuring vowel formant bandwidths. J Acoust Soc Am 33(12):1737–1746

    Article  Google Scholar 

  6. Fant G (1960) Acoustic theory of speech production. Mouton, The Hague

    Google Scholar 

  7. Miller RL (1959) Nature of the vocal chord wave. J Acoust Soc Am 31:667–677

    Article  Google Scholar 

  8. Wong DY, Markel JD, Gray AH (1979) Glottal inverse filtering from the acoustic speech waveform. IEEE Trans Acoust Speech Signal Process 27(4):350–355

    Article  Google Scholar 

  9. Quatieri TF (2004) Discrete-time speech signal processing, principles and practice. Pearson Education, Upper Saddle river

    Google Scholar 

  10. Rabiner LR, Shafer RW (1989) Digital signal processing of speech signals. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  11. Gold B, Morgan N (2002) Speech and audio signal processing. Wiley, New York

    Google Scholar 

  12. Makhoul J (1975) Linear prediction: a tutorial review. In. Proceedings of the IEEE, vol 64, pp 561–580

    Google Scholar 

  13. Atal BS (1974) Effectiveness of linear prediction characteristics of the speech wave for automatic speaker identification and verification. J Acoust Soc Am 55:1304–1312

    Article  Google Scholar 

  14. Teager HM (1980) Some observations on oral air flow during phonation. IEEE Trans Speech Audio Process 28(5):599–601

    Article  Google Scholar 

  15. Campbell J (1997) Speaker recognition: a tutorial. Proc IEEE 511(9):1437–1462

    Article  Google Scholar 

  16. Honda K (2008) Physiological processes of speech production. Springer, Berlin

    Google Scholar 

  17. Hermansky H (1990) Perceptual linear prediction analysis for speech. J Acoust Soc Am 87:1738–1752

    Article  Google Scholar 

  18. Rosenberg AE, Sambur MR (1975) New techniques for automatic speaker verification. IEEE Trans Acoust Speech Signal Process 23(2):169–176

    Article  Google Scholar 

  19. Deng L, O’Shaughnessy D (2003) Speech processing a dynamic and optimization-oriented approach. Marcel Dekker, New York

    Google Scholar 

  20. Tanizaki H (1996) Nonlinear filters—estimation and applications, 2nd edn. Springer, Berlin

    MATH  Google Scholar 

  21. Ghahramani Z, Roweis S (1999) Learning nonlinear dynamic systems using an em algorithm. Adv Neural Inf Process Syst 11:1–7

    Google Scholar 

  22. Segall A (1976) Stochastic processes in estimation theory. IEEE Trans Inf Theory IT-22:275–286

    Article  MathSciNet  Google Scholar 

  23. Tong H (1990) Non-linear time series—a dynamical system approach. Oxford University Press, Oxford

    Google Scholar 

  24. Papoulis A (1984) Probability, random variables and stochastic processes. McGraw-Hill, New York

    Google Scholar 

  25. Kantner M (1979) Lower bounds for nonlinear prediction error in moving avarage processes. Ann Prob 7(1):128–138

    Article  Google Scholar 

  26. Casdagli M, jardins D, Eubank S, Farmer JD, Gibson J, Theiler J, Hunter N (1992) Nonlinear modeling of chaotic time series: theory and applications. In: Kim J, Stringer J (eds) Applied chaos. Wiley, New York, pp 335–380

    Google Scholar 

  27. Farmer JD, Sidorowich JJ (1988) Exploiting chaos to predict the future and reduce noise. In: Lee YC (ed) Evolution, learning, and cognition. World Scientific, Singapore, pp 277–330

    Google Scholar 

  28. Sicuranza GL (1992) Quadratic filters for signal processing. In: Proceedings of IEEE, vol 80, pp 1263–1285

    Google Scholar 

  29. Thyssen J, Nielsen H, Hansen SD (1994) Non-linear short term prediction in speech coding. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’94), Adelaide, pp I-185–I-188

    Google Scholar 

  30. Singer AC, Wornell GW, Oppenheim AV (1994) Nonlinear autoregressive modeling and estimation in the presence of noise. Dig Signal Process 4:207–221

    Article  Google Scholar 

  31. Priestley MB (1988) Non-linear and non-stationary time series analysis. Academic Press, London

    Google Scholar 

  32. Birgmeier M (1995) A fully kalman-trained radial basis function network for nonlinear speech modeling. In: Proceedings of IEEE international conference on neural networks, (ICNN’95), Perth

    Google Scholar 

  33. Birgmeier M (1996) Nonlinear prediction of speech signals using radial basis function networks. In: EUSIPCO’96, vol 1, pp 459–462

    Google Scholar 

  34. de Maria FD, Figueiras AR (1995) Radial basis functions for nonlinear prediction of speech in analysis-by-synthesis coders. In: Proceedings of IEEE workshop on nonlinear signal and image processing, Halkidiki

    Google Scholar 

  35. Lapedes A, Farber R (1998) How neural nets work. In: Lee YC (ed) Evolution, learning, and cognition. World Scientific, Singapore, pp 231–346

    Google Scholar 

  36. Tishby N (1990) A dynamical systems approach to speech processing. In: Proceedings of IEEE international conference on acoustics, speech, and, signal processing (ICASSP’90)

    Google Scholar 

  37. Wu L, Niranjan M, Fallside F (1994) Fully vector quantized neural network-based code-excited nonlinear predictive speech coding. IEEE Trans Speech Audio Process 2(4):482–489

    Google Scholar 

  38. Haykin S, Li L (1995) Nonlinear adaptive perdiction of nonstationary signals. Signal Process 43:526–535

    Google Scholar 

  39. Wu L, Niranjan M (1994) On the design of nonlinear speech predictors with recurrent nets. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’94), Adelaide, pp II-529–II-532

    Google Scholar 

  40. Lorenz EN (1969) Atmospheric predictability as revealed by naturally occurring analogues. J Atmos Sci 26:636–646

    Article  Google Scholar 

  41. Bogner RE, Li T (1989) Pattern search prediction of speech. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’89), Glasgow, pp 180–183

    Google Scholar 

  42. Yakowitz S (1987) Nearest neighbor methods for time series analysis. J Time Ser Anal 8(2):235–247

    Article  MathSciNet  MATH  Google Scholar 

  43. Gersho A (1989) Optimal nonlinear interpolative vector quantization. IEEE Trans Comm 38(9):1285–1287

    Article  Google Scholar 

  44. Lee Y, Johnson D (1993) Nonparametric prediction of non-gaussian time series. In: Proceedings of IEEE international conference on acoustics, speech, and signal processing (ICASSP’93), Minneapolis, MN, pp IV-480–IV-483

    Google Scholar 

  45. Rao BLSP (1983) Nonparametric functional estimation. Academic Press, Orlando

    MATH  Google Scholar 

  46. Kubin G (1995) Nonlinear processing of speech. In: Kleijn WB, Paliwal KK (eds) Speech coding and synthesis. Elsevier Science, Amsterdam

    Google Scholar 

  47. Bishop C (1997) Neural networks for pattern recognition. Clarendon Press, Oxford

    Google Scholar 

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Holambe, R.S., Deshpande, M.S. (2012). Linear and Dynamic System Model. In: Advances in Non-Linear Modeling for Speech Processing. SpringerBriefs in Electrical and Computer Engineering(). Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1505-3_3

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  • DOI: https://doi.org/10.1007/978-1-4614-1505-3_3

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