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We consider the problem of computing the DFT and present two reductions over the standard formula. In the special case of an N-point sequence with N = 2l, the number of multiplications per output point required by this algorithm is, at most, N/4 - 1 and, on the average, N/6 - 1. Each output point requires no more than N - 1 additions. In applications requiring only some of the output points, a computational savings over the standard (FFT) techniques may be achieved. Furthermore, we argue that in a certain sense these reductions are optimal.