A new approach for inference based on treating sampled functions is presented. Sampled functions can be transformed into only a few points by wavelet analysis, thus the complete function is represented by these several discrete points. The finiteness of the teaching samples and the resulting sparse rule bases can be handled by fuzzy rule interpolation methods, like KH interpolation. Using SHDSL transmission performance prediction as an example, the simplification of inference problems based on large, sampled vectors by wavelet transformation and fuzzy rule interpolation applied on these vectors are introduced in this paper.