Mathematics foundations for signal processing system synthesis through generalized Fibonacci interconnection topologies

Abstract

In this paper, we extend various bit-level and wordlevel expressions for representation of switching functions, as SOPs, Reed-Muller expressions, arithmetic, and Walsh expressions, to functions used in Fibonacci interconnection topologies. The corresponding Fibonacci Decision diagrams (FibDDs) are used as graphic representations of these expressions. At the same time, FibDDs are used as a data structure to efficiently calculate coefficients in the introduced expressions, and to perform design of related networks. In this way, we provide a base to extend the application of powerful CAD design tools for switching functions to functions in Fibonacci interconnection topologies.