One-sided spectral density of a real stationary time series
= One-sided spectral density of a real stationary time series
{title2=$\gamma_k=\int_0^\pi f(\omega)\cos(k\omega)\,d\omega$}
= One-sided spectral density
{synonym}
For real stationary processes, the one-sided density on $[0,\pi]$ is twice the usual two-sided density. Its integral is the <variance> and $\gamma_k=\int_0^\pi f(\omega)\cos(k\omega)\,d\omega$. When <covariances> are absolutely summable, $f(\omega)=\pi^{-1}(\gamma_0+2\sum_{k\ge1}\gamma_k\cos(k\omega))$.