Nonlinear analysis of speech signals: generalized dimensions and lyapunov exponents

In this paper, we explore modern methods and algorithms from fractal/chaotic systems theory for modeling speech signals in a multidimensional phase space and extracting characteristic invariant measures like generalized fractal dimensions and Lyapunov exponents. Such measures can capture valuable information for the characterisation of the multidimensional phase space - which is closer to the true dynamics - since they are sensitive to the frequency with which the attractor visits different regions and the rate of exponential divergence of nearby orbits, respectively. Further we examine the classification capability of related nonlinear features over broad phoneme classes. The results of these preliminary experiments indicate that the information carried by these novel nonlinear feature sets is important and useful.

[1]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[2]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[3]  Martin A. Riedmiller,et al.  A direct adaptive method for faster backpropagation learning: the RPROP algorithm , 1993, IEEE International Conference on Neural Networks.

[4]  P. Maragos,et al.  Fractal dimensions of speech sounds: computation and application to automatic speech recognition. , 1999, The Journal of the Acoustical Society of America.

[5]  Francis Sullivan,et al.  Efficient Algorithms for Computing Fractal Dimensions , 1986 .

[6]  Steve McLaughlin,et al.  Speech characterization and synthesis by nonlinear methods , 1999, IEEE Trans. Speech Audio Process..

[7]  U. Parlitz,et al.  Lyapunov exponents from time series , 1991 .

[8]  H. M. Teager,et al.  Evidence for Nonlinear Sound Production Mechanisms in the Vocal Tract , 1990 .

[9]  A. Politi,et al.  Statistical description of chaotic attractors: The dimension function , 1985 .

[10]  Petros Maragos,et al.  Speech analysis and feature extraction using chaotic models , 2002, 2002 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[11]  Gernot Kubin,et al.  Synthesis and coding of continuous speech with the nonlinear oscillator model , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[12]  Mehmet Emre Çek,et al.  Analysis of observed chaotic data , 2004 .

[13]  H. G. E. Hentschel,et al.  The infinite number of generalized dimensions of fractals and strange attractors , 1983 .

[14]  Iasonas Kokkinos,et al.  Some advances in nonlinear speech modeling using modulations, fractals, and chaos , 2002, 2002 14th International Conference on Digital Signal Processing Proceedings. DSP 2002 (Cat. No.02TH8628).

[15]  T. J. Thomas.  A finite element model of fluid flow in the vocal tract , 1986 .

[16]  Martin Casdagli,et al.  Nonlinear Modeling And Forecasting , 1992 .

[17]  Eckmann,et al.  Liapunov exponents from time series. , 1986, Physical review. A, General physics.