Neural Networks for Signal Processing in Measurement Analysis and Industrial Applications : the Case of Chaotic Signal Processing

This chapter discusses the use of neural networks for signal processing. In particular, it focuses on one of the most interesting and innovative areas: the chaotic time series processing. This includes time series analysis, identification of chaotic behavior, forecasting, and dynamic reconstruction. An overview of chaotic signal processing both by conventional and neural network methods is given.

[1]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[2]  Zeng,et al.  Estimating the Lyapunov-exponent spectrum from short time series of low precision. , 1991, Physical review letters.

[3]  Erkki Oja,et al.  Independent component analysis: algorithms and applications , 2000, Neural Networks.

[4]  H. Schuster.  Deterministic chaos: An introduction , 1984 .

[5]  Antonia J. Jones,et al.  Automated embedding and the creep phenomenon in chaotic time series by , 2000 .

[6]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

[7]  I. Johnstone,et al.  Wavelet Shrinkage: Asymptopia? , 1995 .

[8]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[9]  Joachim Holzfuss,et al.  Approach to error-estimation in the application of dimension algorithms , 1986 .

[10]  James P. Crutchfield,et al.  Geometry from a Time Series , 1980 .

[11]  S. Haykin.  Signal processing: where physics and mathematics meet , 2001, IEEE Signal Process. Mag..

[12]  L. Tsimring,et al.  The analysis of observed chaotic data in physical systems , 1993 .

[13]  P. Grassberger,et al.  Measuring the Strangeness of Strange Attractors , 1983 .

[14]  M. Rosenstein,et al.  Reconstruction expansion as a geometry-based framework for choosing proper delay times , 1994 .

[15]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[16]  T. Sauer,et al.  Correlation dimension of attractors through interspike intervals , 1997 .

[17]  Anders Krogh,et al.  Introduction to the theory of neural computation , 1994, The advanced book program.

[18]  Erkki Oja,et al.  Neural Networks, Principal Components, and Subspaces , 1989, Int. J. Neural Syst..

[19]  Alexander H. Waibel,et al.  Modular Construction of Time-Delay Neural Networks for Speech Recognition , 1989, Neural Computation.

[20]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[21]  D. Kugiumtzis.  State space reconstruction parameters in the analysis of chaotic time series—the role of the time window length , 1996, comp-gas/9602002.

[22]  Schwartz,et al.  Singular-value decomposition and the Grassberger-Procaccia algorithm. , 1988, Physical review. A, General physics.

[23]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[24]  G. Lewicki,et al.  Approximation by Superpositions of a Sigmoidal Function , 2003 .