The radix-r one stage FFT kernel computation

The FFT process is an operation that could be performed through different stages. In each stage, the butterfly operation is computed in which the accessed data is multiplied by certain W^alpha, added or subtracted and finally it is stored or held for further processing. This process is repeated to each stage until the final stage where the processed data is driven to the output. In this paper, an appropriate indexing or mapping schemes between the input data and the coefficient multipliers throughout the different stages are yield to a computation single stage by collapsing all stages into a computation single stage. The result is a reduction of communication load and arithmetic operations.