A mixed-radix 4-2 butterfly with simple bit reversing for ordering the output sequences

In recent years, the fast Fourier transform (FFT) has been playing a very important role in the design and implementation of the discrete-time signal processing system. Therefore, various FFT algorithms have been proposed in this area over the last decades. Especially, the pipeline algorithms have been regarded as suitable algorithms for processing high-speed data. Up to now, several pipeline FFT algorithms such as the radix-2ⁱ, the split-radix and the mixed-radix have been proposed. In this paper, we developed a mixed-radix 4-2 butterfly structure with simple bit reversing output sequences derived by index decomposition technique which was used in the radix-2ⁱ algorithm. Compared with the radix-2³ algorithm and the split-radix 2/4/8 algorithm, the proposed algorithm has the same number of multipliers and the less number of the stages and the butterflies than the radix-2³ and the split-radix 2/4/8 algorithm. Moreover, the proposed algorithm makes an offer of the simple bit reversing for ordering the output sequences which is only supported by a fixed-radix FFT algorithm