I want to understand NIST Statistical Test Suite tests. Here (https://arxiv.org/pdf/nlin/0401040.pdf) you can read a derivation of spectral test. There are considered two random variables: $$ \begin{aligned} & c_j=\sum_{k=1}^n x_k \cos \left(2 \pi \frac{(k-1)}{n} j\right) \\ & s_j=\sum_{k=1}^n x_k \sin \left(2 \pi \frac{(k-1)}{n} j\right) . \end{aligned} $$ Then, the authors state:
Here, we can simply prove that $c_j$ and $s_j$ converge to the normal distribution whose mean $\mu$ is zero and variance $\sigma$ is $n/2$ under the assumption of $x_k$ ($−1$ or $+1$ for $k = 1, 2, \ldots , n$) randomness.
How to "simple prove" it? I need an explanation. What kind of convergence it is?