The cyclotomic fast Fourier transform is a type of fast Fourier transform algorithm over finite fields.[1] This algorithm first decomposes a DFT into several circular convolutions, and then derives the DFT results from the circular convolution results. When applied to a DFT over , this algorithm has a very low multiplicative complexity. In practice, since there usually exist efficient algorithms for circular convolutions with specific lengths, this algorithm is very efficient.[2]
^S.V. Fedorenko and P.V. Trifonov, Fedorenko, S. V.; Trifonov, P. V.. (2003). "On Computing the Fast Fourier Transform over Finite Fields" (PDF). Proceedings of International Workshop on Algebraic and Combinatorial Coding Theory: 108–111.
^Wu, Xuebin; Wang, Ying; Yan, Zhiyuan (2012). "On Algorithms and Complexities of Cyclotomic Fast Fourier Transforms Over Arbitrary Finite Fields". IEEE Transactions on Signal Processing. 60 (3): 1149–1158. doi:10.1109/tsp.2011.2178844.
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