"Any sufficiently advanced technology is, of course, indistinguishable from magic".Arthur C Clark.

The graph below says it all. The solid black line is the

matrix algorithm known to Gauss in 1805. The dashed line underneath it is the famous Cooley-Tukey algorithm of 1965 with complexityO(n^{2}). This algorithm is widely credited asO(n.log(n))"... the single breakthrough that made modern signal processing a practical proposition ...". All the other black lines are the results of various other algorithms and optimisations developed since 1965.The red line is the VFFT of 2003 with complexity

. What made the big difference for the Cooley-Tukey algorithm was theO(n)change in slopeon the graph. All the refinements didn't change the slope any more, they just lowered the curve a bit on the vertical axis. But, like the Cooley-Tukey, the VFFT againchanges the slopeof the line.Remember the paradigm shift that Cooley-Tukey made possible. You are now looking at the next one.

Go imagine.