Tactile sensing endows the robots to perceive certain physical properties of the object in contact. Robots with tactile perception can classify textures by touching. Interestingly, textures of fine micro-geometry beyond the nominal resolution of the tactile sensors can also be identified through exploratory robotic movements like sliding. To study the problem of fine texture classification, we design a robotic sliding experiment using a finger-shaped multi-channel capacitive tactile sensor. A feature extraction process is presented to encode the acquired tactile signals (in the form of time series) into a low dimensional (≤7D) feature vector. The feature vector captures the frequency signature of a fabric texture such that fabrics can be classified directly. The experiment includes multiple combinations of sliding parameters, i.e., speed and pressure, to investigate the correlation between sliding parameters and the generated feature space. Results show that changing the contact pressure can greatly affect the significance of the extracted feature vectors. Instead, variation of sliding speed shows no apparent effects. In summary, this paper presents a study of texture classification on fabrics by training a simple k-NN classifier, using only one modality and one type of exploratory motion (sliding). The classification accuracy can reach up to 96%. The analysis of the feature space also implies a potential parametric representation of textures for tactile perception, which could be used for the adaption of motion to reach better classification performance.