 In practice, actual performance on modern computers is usually dominated by factors other than the speed of arithmetic operations and the analysis is a complicated subject (for example, see Frigo & Johnson, 2005), but the overall improvement from formula_1 to formula_2 remains.By far the most commonly used FFT is the Cooley–Tukey algorithm.This is a divide and conquer algorithm that recursively breaks down a DFT of any composite size "N" = "N"1"N"2 into many smaller DFTs of sizes "N"1 and "N"2, along with O("N") multiplications by complex roots of unity traditionally called twiddle factors (after Gentleman and Sande, 1966).