A frequency method of optimal digital redesign of an existing continuous-time system by a quadratic criterion is presented. The method is based on the use of Laplace transformation in continuous time and a parameterization of the set of admissible controllers. The proposed technique makes it possible to solve the optimization problem directly employing input-output relations without an auxiliary passage to the state space. With such an approach the synthesis procedure often gets greatly simplified, The method has the important feature that pure delays in the digital redesigned system can be taken into account in a simple way. It is shown that the presented method can be generalized onto different LQ-optimization problems for sampled-data systems.