Generalized Fibonacci cubes and trees for DSP applications

We present a new interconnection topology called generalized Fibonacci cubes, which unifies a wide range of connection topologies such as the Boolean cube (or hypercube), classical Fibonacci cube, etc. We study the properties of generalized Fibonacci corresponding codes, e.g. we find an Zeckendorfs' theorem for the generalized Fibonacci codes. Some basic properties of generalized Fibonacci cubes and graphs, especially, their topological properties, are also established. Finally, the classes of unitary generalized Fibonacci-Walsh and Fibonacci-Haar transforms are proposed for which efficient computation algorithms and corresponding generalized Fibonacci flowcharts are presented.