Attractor Reconstruction and Dimensional Analysis of Chaotic Signals

  • H. Atmanspacher
  • H. Scheingraber
  • W. Voges
Part of the Ettore Majorana International Science Series book series (EMISS, volume 40)


Traditional techniques of signal analysis are restricted to investigations in the time and frequency domain. They are based on the statistical procedure of deriving the covariance matrix of a time signal as well as the corresponding Fourier transform, the power spectrum. These techniques have been extensively and successfully used in many different scientific branches. In particular, they are very helpful in distinguishing stationary, periodic, and quasiperiodic processes from nonperiodic ones. In the latter case, the temporal correlations generally vanish for t → ∞, and the power spectrum is continuous:
$$ \matrix{ {P(\omega ) >0} & {\forall \omega } \cr }$$
The correlation function for periodic processes does not vanish, and the power is distributed over a (more or less) discrete spectrum:
$$ P(\omega ) = \sum\limits_k {{c_k}\delta } (\omega -{\omega _k})$$
where the c k are the coefficients of the Fourier series representing the correlation function. The discrete spectrum provides the number k of frequencies equivalent to the number of independent variables (degrees of freedom) of the system.


Phase Portrait Dimensional Analysis Chaotic Attractor Chaotic Signal Fractal Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • H. Atmanspacher
    • 1
  • H. Scheingraber
    • 1
  • W. Voges
    • 1
  1. 1.Max-Planck-Institut für extraterrestrische PhysikGarchingGermany

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