If $s_1,\ldots,S_{N-1}\in\mathbb R^n$, then the Fourier transform of $$s(x)=\sum_{i=0}^{N-1}\delta(x-x_i)$$ is given by $$F(f)=\sum_{i=0}^{N-1}e^{-{\rm i}2\pi\langle f,s_i\rangle}.$$ Now, in eq. (2) in this paper, there is the following expression for the squared magnitued of $F(f)$ which I don't understand:
Where does the factor $\frac1N$ come from?