The purpose of our research is to get further improvement in the performance of order statistic filters. The basic idea found in our research is the use of a robust median estimator to obtain median differential order information which the classes of order statistic filter required in order to sort the input signal in the filter window. In order to give the motivation for using a median estimator in the classes of order statistic filters, we derive theorems characterizing the median filters and prove them theoretically using the characteristic that the order statistic filter has the performance for a monotonic signal equivalent with the FIR linear filter. As an application of median operation, we propose and investigate the Median Differential Order Statistic Filter to reduce impulsive noise as well as Gaussian noise and regard it as a subclass of the Order Statistic Filter. Moreover, we introduce the piecewise linear function in the Median Differential Order Statistic Filter to improve performance in terms of edge preservation. We call it the Piecewise Linear Median Differential Order Statistic Filter. The effectiveness of proposed filters is verified theoretically by computing the output Mean Square Error of the filters in parts of edge signals, impulsive noise, small amplitude noise and their combination. Computer simulations also show that the proposed filter can improve the performance in both noise (small-amplitude Gaussian noise and impulsive noise) reduction and edge preservation for one-dimensional signals.