We show that a Z-transform-based time-response analysis of the electro-optical response of a crystal to a step voltage with a short rise time allows one to obtain the dispersion of the electro-optical coefficients over a wide frequency range. We describe the method employed and present the results obtained for the main electroptic coefficients (r22, r61, and rc) of a standard LiNbO3 crystal. We also show that this method is able to provide even small values of the electro-optic coefficient as well as the dispersion within a wide frequency range, which is limited only by the rise time of the step voltage.