  An exponential frequency power spectral density is a well known property of
many continuous time chaotic systems and has been attributed to the presence of
Lorentzian-shaped pulses in the time series of the dynamical variables. Here a
stochastic model of such fluctuations is presented, describing these as a
super-position of pulses with fixed shape and constant duration. Closed form
expressions are derived for the lowest order moments, auto-correlation function
and frequency power spectral density in the case of periodic pulse arrivals and
a random distribution of pulse amplitudes. In general, the spectrum is a Dirac
comb located at multiples of the inverse periodicity time and modulated by the
pulse spectrum. For Lorentzian-shaped pulses there is an exponential modulation
of the Dirac comb. Deviations from strict periodicity in the arrivals
efficiently removes the Dirac comb, leaving only the spectrum of the pulse
function. This effect is also achieved if the pulse amplitudes are independent
of the arrivals and have vanishing mean value. Randomness in the pulse arrival
times is investigated by numerical realizations of the process, and the model
is used to describe the power spectral densities of time series from the Lorenz
system.
