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MORPHOLOGICAL PSEUDOCONVOLUTIONS ARE MORPHOLOGICAL FILTERS DERIVED FROM MOVING STATISTICAL FILTERS SUCH AS MOVING AVERAGES AND MOVING MEDIANS. THIS PAPER DISCUSSES FAMILIES OF OPERATING CHARACTERISTIC CURVES FOR THREE COMMON FILTERING PROBLEMS: SUPPRESSION OF WHITENOISE, PRESERVATION OF STEPS, AND PRESERVATION OF LOW BACKGROUND VARIATION. GIVEN THE NOISE STATISTICS, AND GIVEN DESIRABLE FILTERING BEHAVIOR, ONE CAN EMPLOY THE PROPER OPERATING CHARACTERISTIC CURVES.