Accurate and fast measurements are important in many areas of everyday engineering and research activities. This paper proposes a method that gives such measurements, additionally shortening the time in which they are obtained. To achieve this, a supplementary discrete-time filter, estimating values of delayed samples of the measured signal, is attached to the output of the data acquisition system. This filter is identified with the use of classical estimation methods, based on a dynamical model of the data acquisition system. The definition of the cost function minimised during filter identification depends on the nature of the environment in which measurements are acquired. The considerations presented in this paper are illustrated with four corresponding simulated case study examples. They show how, in a very simple way, dynamical properties of data acquisition systems may be corrected, and thus improved, using the corresponding supplementary discrete-time filters. The improvement, measured by the correction quality index introduced in the paper, was from a few times up to more than 100. The paper also raises the issue of obtaining models for tuning of the supplementary discrete-time filter. The considerations presented may be applied to formulate the artificial intelligence of data acquisition systems as well as sensors. Finally, the paper proposes to implement this intelligence as a knowledge base of the expert system.