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The Discrete Pulse Transform (DPT) for images and videos has been developed over the past few years and provides a theoretically sound setting for a nonlinear decomposition of an image or video. In [1] the theoretical basis of the DPT was presented. In this paper we now present a sound  characterization of this useful nonlinear hierarchical decomposition by referring to its ability as a separator, the consistency of the decomposition, as well as the smoothing ability of the decomposition.