Fibonacci spectral transforms: Calculation, algorithms and circuit realizations

Abstract

In this article, we define the Fibonacci decision diagrams (FibDDs) permitting representation of functions defined in a number of points different from N=2n by decision diagrams consisting of nodes with two outgoing edges. We show the relationships between the FibDDs and the contracted Fibonacci codes and propose a procedure for calculation of the generalized Fibonacci transforms through FibDDs. This procedure permits calculation of the generalized Fibonacci spectra of functions defined in a number of points equal to a large generalized Fibonacci number. We use FibDDs to design architectures for realization of discrete functions and calculation of the generalized Fibonacci p-transforms. We also consider the circuit realizations of functions represented by FibDDs and the circuit realizations of Fibonacci spectral transforms.