LTI filtering for wide-sense stationary process
It's basically just about using the definitions and doing the math:

$$\begin{align}R_{WW}[n]&amp;=E\{W^*[k]W[k+n]\}\\
&amp;=E\left\{\sum_mU^*[k-m]h^*[m]\sum_lU[k+n-l]h[l]\right\}\\
&amp;=\sum_m\sum_lh^*[m]h[l]E\left\{U^*[k-m]U[k+n-l]\right\}\\
&amp;=\sum_m\sum_lh^*[m]h[l]R_{UU}[n+m-l]\\
&amp;=\sum_mh^*[m]\sum_lh[l]R_{UU}[n+m-l]\\
&amp;=\sum_mh^*[m]\left(h\star R_{UU}\right)[n+m]\\
&amp;=\sum_mh^*[-m]\left(h\star R_{UU}\right)[n-m]\\
&amp;=h^*[-n]\star h[n]\star R_{UU}[n]\end{align}$$

where $*$ denotes complex conjugation, and $\star$ denotes convolution.