What function $f$ is such that its Fourier coefficients are a normal distribution? that is to say: given some number $s$, write
$$\forall j\in\mathbb{Z}, \ c\_j=e^{-j^2/s}$$
and if
$$\lim\_{N\to\infty} \sum\_{j=-N}^{N} c\_je^{ijt} \to\_{a.e.} f(t) $$
then find $f$.