Signature of chaos in power spectrum |
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Authors: | M C Valsakumar S V M Satyanarayana V Sridhar |
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Institution: | (1) Theoretical Studies Section, Materials Science Division, Indira Gandhi Centre for Atomic Research, 603 102 Kalpakkam, India |
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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/f
2 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. |
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Keywords: | Chaos time series analysis Power spectrum Aliasing |
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