A systematic approach to a class of approximations to the pulse transfer function of a system consisting of a zero-order hold and a Linear continuous-time plant is presented. It is based on the asymptotic result of Astrom, Hagander, and Sternby on zeros of sampled systems at high sampling rates, and on the bilinear transformation. Since the number of intrinsic parameters does not change in the discretization process, model matching control, robust control, and identification are suggested as possible areas of application. Superiority of the approximations considered over a delta-operator based truncated approximation is shown. The results are illustrated by an example.