Twiddle factor

The factor $W_N^k=e^{-i2\pi k/N}$ that scales the odd half's DFT before combining it with the even half's.

A twiddle factor $W_N^k=e^{-i2\pi k/N}$ is the root of unity that scales the odd-indexed half's DFT before it is added to or subtracted from the even-indexed half's, in the Cooley-Tukey recombination step. It is the only genuinely new multiplication the FFT introduces at each recursive level.

Examples

For $N=4$ , the twiddle factors are $W_4^0=1$ and $W_4^1=e^{-i\pi/2}=-i$ .