We investigate the nature of the numerically computed power spectral d
ensity P(f, N, tau) Of a discrete (sampling time interval, tau) and fi
nite (length, N) scalar time series extracted from a continuous time c
haotic dynamical system. We highlight how P(f, N, tau) differs from th
e true power spectrum and from the power spectrum of a general stochas
tic process. Non-zero tau leads to aliasing; P(f, N, tau) decays at hi
gh frequencies as [pi tau/sin pi tau f](2), which is an aliased form o
f the 1/f(2) decay. This power law tail seems to be a characteristic f
eature of all continuous time dynamical systems, chaotic or otherwise.
Also the tail vanishes in the limit of N --> infinity, implying that
the true power spectral density must be band width limited. In strikin
g contrast the power spectrum of a stochastic process is dominated by
a term independent of the length of the time series at all frequencies
.