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The iterative truncated arithmetic mean (ITM) filter has been recently proposed. It possesses merits of both the mean and median filters. In this brief, the Cramer-Rao lower bound is employed to further analyze the ITM filter. It shows that this filter outperforms the median filter in attenuating not only the short-tailed Gaussian noise but also the long-tailed Laplacian noise. A fast realization of the ITM filter is proposed. Its computational complexity is studied. Experimental results demonstrate that the proposed algorithm is faster than the standard median filter.