Let $\boldsymbol{X} = (X_n)_{n\in \mathbb{Z}}$ be a zero-mean real valued stationary process. Denote $\gamma$ its autocovariance function, i.e.:
\begin{equation} \gamma(h) = \mathbb{E}X_nX_{n+h} \end{equation}
Suppose $\gamma$ is summable, i.e. $\sum_{h \in \mathbb{Z}}|\gamma(h)| < \infty $, then $\boldsymbol{X}$ has a spectral density given by: \begin{equation} f(x) = \sum_{h\in \mathbb{Z}} \gamma(h)e^{-2 \pi i h x} \end{equation} where $x\in \mathbb{R}$, but since $f$ is $1-$periodic, we restric its domain to $[-1/2,1/2]$.
It is well known that $f\geq0$. Bradley in its paper 'On the Spectral Density and Asymptotic Normality of Weakly Dependent Random Fields' (see for instance https://link.springer.com/article/10.1007/BF01046741) gave a necessary and sufficient condition to have $f$ continuous and (strictly) positive (see Theorem 2). I have a hard time understanding the quantity $r^{*}$ and how to compute it in practice. Any help or other references on the subject would be greatly appreciated!