In this study, the derivation of the butterfly algorithm is expounded, and the detailed formulas based on Cooley-Tukey algorithm of Fast Fourier transform (FFT) are also presented. On the basis of what is described above, we propose two novel designs of low-cost and high-throughput linear arrays for FFT computations. Compared with popular radix-2/radix-4 structures, the presented radix-2^3/radix-8 architectures reach two to eight times of higher throughput rate. In addition, the proposed design has the features of regularity, modularity, and parallelism. Thus, low hardware complexity can be achieved in VLSI designs.