Summary
Let M(N) denote the number of active multiplications/divisions needed to compute the discrete Fourier transform of N variables. Winograd showed M(N) ≦ O(N). For N a power of two we analyse his method and find M(N)≦8 N−o(N). Using additional symmetries we improve this to M(N)≦2N−o(N). We also give a very short proof for M(N)≦4N-o(N). Finally we show M(N)≧N − 2 log N.
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Mescheder, B. On the number of active *-operations needed to compute the discrete Fourier transform. Acta Informatica 13, 383–408 (1980). https://doi.org/10.1007/BF00288772
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DOI: https://doi.org/10.1007/BF00288772