Matrix factorization derivation and analysis of computational complexity of a new radix-2 DFT algorithm

Recently, a new family of discrete Fourier transform algorithms has been reported in which the structural complexity is significantly reduced without affecting the arithmetic complexity. In the present paper, a radix-a algorithm of this family is derived using the matrix factorization approach. This approach is known to be useful in mapping algorithms to architectures. An analysis of the computational complexity of this algorithm is carried out. A run-time comparison of the proposed algorithm is made with the Cooley-Tukey radix-2 algorithm.