  The auto-correlation function and the frequency power spectral density due to
a super-position of uncorrelated exponential pulses are considered. These are
shown to be independent of the degree of pulse overlap and thereby the
intermittency of the stochastic process. For constant pulse duration and a
one-sided exponential pulse shape, the power spectral density has a Lorentzian
shape which is flat for low frequencies and a power law at high frequencies.
The algebraic tail is demonstrated to result from the discontinuity in the
pulse function. For a strongly asymmetric two-sided exponential pulse shape,
the frequency spectrum is a broken power law with two scaling regions. In the
case of a symmetric pulse shape, the power spectral density is the square of a
Lorentzian function. The steep algebraic tail at high frequencies in these
cases is demonstrated to follow from the discontinuity in the derivative of the
pulse function. A random distribution of pulse durations is shown to result in
apparently longer correlation times but has no influence on the asymptotic
power law tail of the frequency spectrum. The effect of additional random noise
is also discussed, leading to a flat spectrum for high frequencies. The
probability density function for the fluctuations is shown to be independent of
the distribution of pulse durations. The predictions of this model describe the
variety of auto-correlation functions and power spectral densities reported
from experimental measurements in the scrape-off layer of magnetically confined
plasmas.
