A new discrete Fourier transform algorithm using butterfly structure fast convolution

This paper proposes a new approach to computing the discrete Fourier transform (DFT) with the power of 2 length using the butterfly structure number theoretic transform (NTT). An algorithm breaking down the DFT matrix into circular matrices with the power of 2 size is newly introduced. The fast circular convolution, which is implemented by the NTT based on the butterfly structure, can provide significant reductions in the number of computations, as well as a simple and regular structure, The proposed algorithm can be successively implemented following a simple flowchart using the reduced size submatrices. Multiplicative complexity is reduced to about 21 percent of that by the classical FFT algorithm, preserving almost the same number of additions.