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Details on its internal operation will be found in the paper by Cooley and Tukey and in other sources. This is why the fast Fourier transform is called fast and why it has revolutionized the digital processing of waveforms. If N = 1 0 2 4 ( 2 1 0), the fast Fourier transform achieves a computational reduction by a factor of over 200. For N a power of 2, the fast Fourier transform technique of Cooley and Tukey cuts the number of multiplications required to ( N / 2 ) log 2 N. Because of the tremendous increase in speed achieved (and reduction in cost), the fast Fourier transform has been hailed as one of the few really significant advances in numerical analysis in the past few decades.įor N data points, a direct calculation of a discrete Fourier transform would require about N 2 multiplications. The reduction is possible because the transformation matrix contains large numbers of duplicate entries, and the FFT procedure organizes the computation in a way permitting identical sets of coefficients to be computed only once. Brought to the attention of the scientific community by Cooley and Tukey, 4 its importance lies in the drastic reduction in the number of numerical operations required. The fast Fourier transform (FFT) is a particular way of factoring and rearranging the terms in the sums of the discrete Fourier transform. Harris, in Mathematical Methods for Physicists (Seventh Edition), 2013 Fast Fourier Transform