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In this correspondence, we analyze the root structures of the standard median (SM) filters, the recursive median (RM) filters, and the FIR median hybrid (FMH) filters. It is shown that these filters have many oscillatory infinitely long root signals. When a section of an oscillatory root is present in a signal, the filter's noise attenuation of the filter is not as good as predicted by statistical measures. We also suggest methods to prevent the possible harmful effect caused by the existence of these roots.