Positive-frequency spectral normalization
= Positive-frequency spectral normalization
{title2=$g(\omega)=2f(\omega)$}
For a real <weakly stationary process>, restricting its even angular-frequency density $f$ to $[0,\pi]$ gives $\gamma(k)=2\int_0^\pi f(\omega)\cos(k\omega)\,d\omega$. Folding both frequency halves into one density gives $g=2f$ and removes that factor two. Consequently <white noise> of variance $v$ has restricted density $v/(2\pi)$ and folded density $v/\pi$.