Parallel Algorithms for Fast Fourier Transformation Using PowerList , ParList and PList Theories (Research Note)

Data structures PowerList, ParList and PList are efficient tools for functional descriptions of parallel programs, that are divide and conquer in nature. PowerList data structures were introduced by J. Misra, and then, J. Kornerup extend these structures to ParList and PList structures. In the introduction of this article these theories are briefly explained. The goal of this work is to develop three parallel variants for Fast Fourier Transformation, using these theories. The variants are implied by the coefficients number of the polynomial, which can be a power of two, a prime number, or a product of prime factors. The last variant, includes the first two, and represents a general and efficient parallel algorithm for Fast Fourier Transformation. This general algorithm has a very good time complexity and can be mapped on a recursive interconnected network.