 This method (and the general idea of an FFT) was popularized by a publication of Cooley and Tukey in 1965, but it was later discovered that those two authors had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805 (and subsequently rediscovered several times in limited forms).The best known use of the Cooley–Tukey algorithm is to divide the transform into two pieces of size "N"/2 at each step, and is therefore limited to power-of-two sizes, but any factorization can be used in general (as was known to both Gauss and Cooley/Tukey).These are called the "radix-2" and "mixed-radix" cases, respectively (and other variants such as the split-radix FFT have their own names as well).