A scheme is presented in the paper for the digital identification of a continuous-time system. The proposed identifier operates on a sampled data system but generates an estimate of the unknown continuous-time system directly. Convergence results are obtained and are independent of the sampling rate and the knowledge of input-output signals between sampling instants. Also discussed in the paper are some related problems. In particular, the convergence of the identifier requires the persistent excitation (PE) condition on certain signals, and that PE condition is reduced to the controllability and observability of the sampled system of an unknown continuous-time system. Moreover, results are derived concerning the controllability and observability of the sampled data system for an unknown continuous-time system.