Recent developments in Haar wavelet transform for application to switching and multivalued logic functions representations

Abstract

In many instances, classical approaches in switching theory and logic design require brute force search procedures. Application of spectral transforms often provides a promising solution of the problem. In particular, the discrete Haar transform appears very interesting for such applications for its wavelet-like properties and fast calculation algorithms. The chapter briefly reviews recent development in this area and is intended to provide compact representations of discrete functions including switching and multivalued logic functions as examples. To this end, decision diagrams are treated in terms of the Haar transform and an algorithm for reduction of the number of paths and the size of such diagrams is described with potential applications to the problems of circuit verification and testing. These representations of multi-output switching functions can be a basis for efficient realizations and various other applications. For instance, word-level representations, including Haar series representations of switching functions and related decision diagrams, are useful in fast prototyping by LUT-FPGAs and in hardware-software codesign. Then, an extension of definitions of Haar spectral transform diagrams to multivalued functions is provided. It is shown that these decision diagrams determine a large class of multivalued Haar functions and related transforms.