Generating realistic texture feelings on tactile displays using data- driven methods has attracted a lot of interest in the last decade. However, the need for large data storages and transmission rates complicates the use of these methods for the future commercial displays. In this paper, we propose a new texture rendering approach which can compress the texture data significantly for electrostatic displays. Using three sample surfaces, we first explain how to record, analyze and compress the texture data, and render them on a touchscreen. Then, through psychophysical experiments conducted with nineteen participants, we show that the textures can be reproduced by a significantly less number of frequency components than the ones in the original signal without inducing perceptual degradation. Moreover, our results indicate that the possible degree of compression is affected by the surface properties.