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