Current methods of pulse sampling are limited in their ability to sample efficiently when both the pulse shapes and their locations are unknown, treating the multi-pulse signals like any other time-limited signal, not taking sparseness into account, and collecting unnecessary samples. The presented technology allows for recovery of multi-pulse signals at sub-Nyquist rates with high precision from a small number of measurements without the need for any prior knowledge of position and shape. This system can be applied to many fields, including radar, ultrasound, communication and medical imaging signals.