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Sliding a probe over a textured surface generates a rich collection of vibrations that one can easily use to create a mental model of the surface. Haptic virtual environments attempt to mimic these real interactions, but common haptic rendering techniques typically fail to reproduce the sensations that are encountered during texture exploration. Past approaches have focused on building a representation of textures using a priori ideas about surface properties. Instead, this paper describes a process of synthesizing probe-surface interactions from data recorded from real interactions. We explain how to apply the mathematical principles of Linear Predictive Coding (LPC) to develop a discrete transfer function that represents the acceleration response under specific probe-surface interaction conditions. We then use this predictive transfer function to generate unique acceleration signals of arbitrary length. In order to move between transfer functions from different probe-surface interaction conditions, we develop a method for interpolating the variables involved in the texture synthesis process. Finally, we compare the results of this process with real recorded acceleration signals, and we show that the two correlate strongly in the frequency domain.