Dragging a tool across a textured object creates rich high-frequency vibrations that distinctly convey the physical interaction between the tool tip and the object surface. Varying one’s scanning speed and normal force alters these vibrations, but it does not change the perceived identity of the tool or the surface. Previous research developed a promising data-driven approach to embedding this natural complexity in a haptic virtual environment: the approach centers on recording and modeling the tool contact accelerations that occur during real texture interactions at a limited set of force-speed combinations. This paper aims to optimize these prior methods of texture modeling and rendering to improve system performance and enable potentially higher levels of haptic realism. The key elements of our approach are drawn from time series analysis, speech processing, and discrete-time control. We represent each recorded texture vibration with a low-order auto-regressive moving-average (ARMA) model, and we optimize this set of models for a specific tool-surface pairing (plastic stylus and textured ABS plastic) using metrics that depend on spectral match, final prediction error, and model order. For rendering, we stably resample the texture models at the desired output rate, and we derive a new texture model at each time step using bilinear interpolation on the line spectral frequencies of the resampled models adjacent to the user’s current force and speed. These refined processes enable our TexturePad system to generate a stable and spectrally accurate vibration waveform in real time, moving us closer to the goal of virtual textures that are indistinguishable from their real counterparts.