Repeat the previous problem for \(x(t)=\exp \left(-t^{2} / 2ight) \cos 2 \pi f_{0} t\).

Data From Problem 10

A pulse train \(y(t)\) is given by

\[
y(t)=\sum_{n=0}^{2} w(n) x\left(t-n \tau^{\prime}ight)
\]

where \(x(t)=\exp \left(-t^{2} / 2ight)\) is a single pulse of duration \(\tau^{\prime}\) and the weighting sequence is \(\{w(n)\}=0.5,1,0.7\}\). Find and sketch the correlations \(\boldsymbol{R}_{x}, \boldsymbol{R}_{w}\), and \(\boldsymbol{R}_{y}\).