  Fluctuations in a vast range of physical systems can be described as a
superposition of uncorrelated pulses with a fixed shape, a process commonly
referred to as a (generalized) shot noise or a filtered Poisson process. In
this contribution, we present a systematic study of a novel deconvolution
method to estimate the arrival times and amplitudes of the pulses from
realizations of such processes. The method shows that time-series can be
reconstructed for various pulse amplitude and waiting time distributions.
Despite a constraint on positive-definite amplitudes, it is shown that negative
amplitudes may also be reconstructed by flipping the sign of the time series.
The method performs well under moderate amounts of additive noise, both white
noise and colored noise having the same correlation function as the process
itself. The estimation of pulse shapes from the power spectrum is accurate
except for excessively broad waiting time distributions. Although the method
assumes constant pulse durations, it performs well under narrowly distributed
pulse durations. The most important constraint on the reconstruction is
information-loss, which limits the method to intermittent processes. The ratio
between the sampling time and the average waiting time between pulses must be
about 1/20 or smaller for a well sampled signal. Finally, given the system
forcing, the average pulse function may be recovered. This recovery is only
weakly constrained by the intermittency of the process.
