Radix 2 FFT

When $N$ is a power of $2$, say $N=2^K$ where $K>1$ is an integer, then the above DIT decomposition can be performed $K-1$ times, until each DFT is length $2$. A length $2$ DFT requires no multiplies. The overall result is called a radix 2 FFT. A different radix 2 FFT is derived by performing decimation in frequency.

A split radix FFT is theoretically more efficient than a pure radix 2 algorithm [71,30] because it minimizes real arithmetic operations. The term ``split radix'' refers to a DIT decomposition that combines portions of one radix 2 and two radix 4 FFTs [20].^A.4On modern general-purpose processors, however, computation time is often not minimized by minimizing the arithmetic operation count (see §A.7 below).