For a class of dynamical systems driven by chaotic impulses we give conditions for the occurrence of chaos locking. The concept of time-discontinuous coupling of two identical chaotic systems is introduced and it is shown how this may lead to synchronization. This method of synchronization is interpreted as a nonlinear analog of the sampling theorem. Furthermore, we examine the effect of amplitude quantization of the driving signal on their synchronization. Even though two time-discontinuously coupled dynamical systems are no more exactly synchronized when the driving signal is digitized, their trajectories are close enough to allow correct transmission of digital information signals between them.