In this paper, we present two different filter-based identification methods to obtain discrete transfer functions for LTI systems under real sampling of finite duration rather than an instantaneous ideal one. The first method is based on a typically used least-squares minimization, while the second one is based on the Leverrier algorithm; that is, using a data series of the impulse response of the system to identify a parametric discrete model. This second method, being also an approximated technique, provides an algebraic result at least for the first computed data of the series. The main idea is to use semi-heuristic techniques of reduced mathematical complexity to derive parametric discrete models from measured input-output data series. These methods are of particular practical interest when the continuous-time system is unknown or when dealing with discrete-time systems whose analytical expression become very complex due, for instance, to the use of finite duration real sampling. This is the case of the problem treated in the application, where the proposed discretization technique allows a simple and accurate description of the discrete system. The identification techniques are also used to improve the discretization process in the context of a bi-estimation scheme that switches to the model that provides a better performance at each considered estimation instant, which is also used to compare the two techniques.