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This article presents an approach to the initialization of the wavelet packet transform (WPT), which is a generalization of the discrete wavelet transform (DWT), by an extension of the interpolatory graphical display algorithm (IGDA). The exact computation of the WPT of functions that are piecewise constant on dyadic intervals is demonstrated. The method is for piecewise constant signals, as the details of how to do this do not appear to be readily available in the open literature. Furthermore, the solution is conveniently placed in a multirate signal processing framework.