Fibonacci decision diagrams and spectral Fibonacci decision diagrams

The authors 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. Then, we define the Spectral Fibonacci DDs (FibSTDDs) in terms of the generalized Fibonacci transforms. This broad family of transforms provides a corresponding family of FibSTDDs. These DDs allow compact representations of functions with simple Fibonacci spectra. Such representations may be useful in various tasks of signal processing, including image processing and systems design, where the generalized Fibonacci transforms have been efficiently used