Suppose we have the autocorrelation function of $X(t)=\sigma^2 cos(w^{'}(\tau ))$, where $w^{'}$ is a constant.
To find the power density spectrum, we calculate $S_{xx} =\int_{-\infty}^{\infty} \sigma^2cos(w^{'}(\tau))e^{-jw\tau} d\tau$.
Without the detailed steps, the provided answer was $\sigma^2 \pi(\delta(w-w^{'})+\delta(w+w^{'}))$ by introducing the new function $\delta$.
Could you please provide the detailed steps to get the answer?
Thank you so much for your help.