Fourier Transform, Optical Computing, Technology, Next Generation Tech.
roots of unity. For instance, if N=2ⁿ​ for some integer n, one can evaluate a Fourier transform of size N by performing n2ⁿ⁻¹​ Fourier transforms of size 2​ and as many complex multiplications. The resulting asymptotic complexity is O(N log N)​, which is much better than the complexity ​O(N²) of