Sub-Nyquist sampling of short pulses

We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. To the best of our knowledge, stable and low-rate sampling strategies for a superposition of unknown pulses without knowledge of the pulse locations have not been derived. 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. Our approach is based on modulating the input signal in each channel with a properly chosen waveform, followed by an integrator. As we show, the resulting scheme is flexible and exhibits good noise robustness.