 As a result, it manages to reduce the complexity of computing the DFT from formula_1, which arises if one simply applies the definition of DFT, to formula_2, where formula_3 is the data size.The difference in speed can be enormous, especially for long data sets where "N" may be in the thousands or millions.In the presence of round-off error, many FFT algorithms are much more accurate than evaluating the DFT definition directly or indirectly.