In some studies involving numerical responses from human subjects (for instance, time allocation studies, and age reporting) an effect called “heaping” is observed. In many cases, such data must be “smoothed” before they can be used. Thus, it is of interest to know the nature of the properties of a frequency function which may be lost in its smoothed version. For those smoothing functions that can be expressed in terms of matrix multiplication; this paper connects properties preserved by the function to properties of its corresponding matrix.