QuestionLet $\{x(t)\}$ be a band$-$limited process with band$-$width $B$ and autocorrelation function $R_x()$ that is

twice differentiable at the origin. Prove that for any $in(-\frac{}{B},\frac{}{B})$ it holds that:

$\frac{2{}^2}{{}^2}|R_x^{}(0)|R_x(0)-R_x()\frac{{}^2}{2}|R_x^{}(0)|,$

where $R_x^{}()\frac{d^2{R}_x()}{d{}^2}.$ Clue: use the inequality $sin()\frac{2}{},AAin[0,\frac{}{2}].$