Comment by briansm

It's interesting that in terms of practical implementations, since each multiply can be done as a series of bit-shifts and additions, and since each element of an FFT is just the solution of a polynomial (a series of multiply-accumulates), in theory it's theoretically possible to do a full FFT in a single cpu clock cycle, much as it's possible to do a single multiply or multiply-accumulate in a single clock cycle (via parallel shift-accumulate operations). It would take a ridiculous number of transistors to implement though.