A pulse train (y(t)) is given by [ y(t)=sum_{n=0}^{2} w(n) xleft(t-n tau^{prime}ight) ] where (x(t)=exp left(-t^{2} /

Question:

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 $\boldsymbol{R}_{y}$.