Effects of Median Filtering on Fractional Processes

Abstract

Median filtering, an effective non-linear signal enhancement technique, has been successfully used for the suppression of impulsive noise and extracting features from noisy signals. Although median filtering can effectively preserve the sharp changes in signals, some signal distortion may be introduced and some features of signals may be lost. In this research, we investigate the effects of median filtering on fractional processes which are characterized by the heavy-tailed distribution or the long-range dependence (LRD). The effects of median filtering on heavy-tailed distribution characteristic of α-stable processes, and on LRD property of long-range dependent processes are investigated, respectively. Besides, the effects of median filtering on both the heavy tailed distribution and the LRD properties of fractional autoregressive integrated moving average (FARIMA) with stable innovations time series are studied. The analysis results show that the heavy-tailed distribution and the LRD properties of fractional processes are evidently affected by median filtering.