Design of Haar wavelet transforms and Haar spectral transform decision diagrams for multiple-valued functions

Abstract

In spectral interpretation, decision diagrams (DDs) are defined in terms of some spectral transforms. For a given DD, the related transform is determined by an analysis of expansion rules used in the nodes and the related labels of edges. The converse task, design of a DD in terms of a given spectral transform often requires decomposition of basic functions in spectral transform to determine the corresponding expansion rules and labels at the edges. We point out that this problem relates to the assignment of nodes in Pseudo-Kronecker DDs (PKDDs). Due to that, we generalize the definition of Haar spectral transform DDs (HSTDDs) to multiple-valued (MV) functions. Conversely, front such defined HSTDDs, we derive various Haar transforms for MV functions.