Design of a multidimensional split vector-radix decimation-in-frequency FFT algorithm

In this paper, the existing one-dimensional (1-D) radix-2/4 decimation-in-frequency (DIF) fast Fourier transform (FFT) algorithm is generalized to the case of an arbitrary dimension by introducing a mixture of radix-(2 times 2 times ... times 2) and radix-(4 times 4 times ... times 4) index maps. The introduction of these index maps coupled with an appropriate use of the Kronecker product enable us to design an efficient multi-dimensional (M-D) split vector-radix DIF FFT algorithm and characterize its butterfly by simple closed-form expressions allowing easy software or hardware implementation of the algorithm for any dimension. It is shown that the proposed algorithm substantially reduces the complexity compared to the existing M-D FFT algorithms