Show that if the autocorrelation function \(K(s)\) of a certain statistically stationary variable \(y(t)\) is given by

\[
K(s)=K(0) \frac{\sin (a s)}{a s} \frac{\sin (b s)}{b s} \quad(a>b>0)
\]

then the power spectrum \(w(f)\) of that variable is given by

\[
\begin{aligned}
& w(f)=\frac{2 \pi}{a} K(0) \quad \text { for } 0& \frac{2 \pi}{a b} K(0)\left\{\frac{a+b}{2}-\pi f\right\} \quad \text { for } \frac{a-b}{2 \pi} \leq f \leq \frac{a+b}{2 \pi}, \\
& 0 \\
& \text { for } \frac{a+b}{2 \pi} \leq f<\infty \text {. }
\end{aligned}
\]

Verify that the function \(w(f)\) satisfies the requirement (15.5.16).