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      https://www.ias.ac.in/article/fulltext/pram/048/01/0069-0085

    • Keywords

       

      Chaos; time series analysis; Power spectrum; Aliasing

    • Abstract

       

      We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]2, which is an aliased form of the 1/f2 decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.

    • Author Affiliations

       

      M C Valsakumar1 S V M Satyanarayana1 V Sridhar1

      1. Theoretical Studies Section, Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam - 603 102, India
    • Dates

       
  • Pramana – Journal of Physics | News

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