The figure below illustrates how the DFT can be computed as a “vector-matrix” multiplication for the size \(N = 16\). Input samples arrive in a 1 x 16 input vector for each transform. This vector is multiplied by a 16 x 16 matrix of DFT twiddle factors to produce a 1 x 16 output vector. This computation requires \(N^2 = 256\) complex multiplications per transform.