  We develop sub-Nyquist sampling systems for analog signals comprised of
several, possibly overlapping, finite duration pulses with unknown shapes and
time positions. Efficient sampling schemes when either the pulse shape or the
locations of the pulses are known have been previously developed. To the best
of our knowledge, stable and low-rate sampling strategies for continuous
signals that are superpositions of unknown pulses without knowledge of the
pulse locations have not been derived. The goal in this paper is to fill this
gap. We propose a multichannel scheme based on Gabor frames that exploits the
sparsity of signals in time and enables sampling multipulse signals at
sub-Nyquist rates. Moreover, if the signal is additionally essentially
multiband, then the sampling scheme can be adapted to lower the sampling rate
without knowing the band locations. We show that, with proper preprocessing,
the necessary Gabor coefficients, can be recovered from the samples using
standard methods of compressed sensing. In addition, we provide error estimates
on the reconstruction and analyze the proposed architecture in the presence of
noise.
