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We consider some generalizations of median filters which combine properties of both the linear and median filters. In particular, L filters and M filters are considered, motivated by robust estimators which are generalizations of the median as a location estimator. A related filter, which we call the modified trimmed mean (MTM) filter, is also described. The filters are evaluated for their performance on noisy signals containing sharp discontinuities or edges. It is shown that M filters can offer a more favorable combination of the running mean and median filters than can L filters, while MTM filters generally have better characteristics than M filters. We also show that an MTM filter is a data-dependent modification of L filters. The concept of double-window filtering is introduced as a refinement of MTM filtering. One representative set of filtered sequences of a test input using these filters are presented to illustrate the performance characterisics of these filters.