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.

We report new results on a dynamical model of serrated yielding. These essentially pertain to the full spectrum of Lyapunov exponents of the non-linear (chaotic) model and fractal characterization of the associated strange attractor. The power spectrum of scalar time series extracted from the phase space trajectories decays exponentially with increase of frequency and the decay constant is found proportional to the Kolmogorov-Sinai entropy.