Based on multiple measurement vectors，a method was proposed to realize the sampling and reconstruction of the sparse signals. According to the feature of periodic non-uniform sampling that needs multiple channels，the sampling and reconstruction of signals were transformed into matrix and vector operations by using the theory of union of subspaces. The necessary condition of reconstruction was analyzed and the complete reconstruction of sparse signal was achieved in the virtue of interpolations, which could insure that the signals could be applied in digital system. Finally, it was proved that the method can achieve the sampling and reconstruction of sparse signals from recovery successful rate and integer of system.
