Properties of discrete time systems obtained by sampling continuous time systems are described. By introducing prefilters, we can treat different ways of sampling within one framework. Results on the convergence of poles and zeros of transfer functions and noise filters as the sampling interval tends to zero are given. These results are generalizations of the results of Åström, Hagander and Sternby (1984) on the convergence of poles and zeros for zero-order hold sampled transfer functions. Sampled noise models are also analysed. Knowledge of these properties is very important in, for example, discrete time simulations of continuous time systems, and identification of continuous time models based on discrete time measurements.