The world of haptics, tactile rendering of textures and tactile interfaces has witnessed significant expansion in the last years. When dealing with the design of tactile devices, the interaction between the device and the user's finger becomes crucial. With a focus on optimizing vibrotactile devices for texture rendering, a parametric analysis of the dynamic transfer function of the human finger was conducted under different test conditions. An average transfer function has been then calculated from the different contact conditions and among several participants. In the tactile rendering process, this average transfer function is exploited, by a tactile device, to reproduce the Friction-Induced Vibrations, previously measured during the exploration of real surfaces. Texture discrimination campaigns have been then performed using both the average transfer function and the specific ones to each participant, in order to reproduce the vibrational stimuli. The results obtained with the averaged transfer function and the participant specific ones were in excellent agreement, highlighting how the development of tactile devises for texture rendering can neglect the variabilities due to the participant finger dynamic response and to the contact boundary conditions.