Question $2$: Consider the signal h$[$n$]$ given by h$[$n$]=1$ n $=01$ n $=40$ otherwise a$)$ Calculate the z$-$transform H$($z$).$ Find its poles and zeros. b$)$ Let H$[$k$]$ be the $512-$point DFT of h$[$n$].$ Show that H$[0]=$ H$[128]=$ H$[256]=$ H$[384]=0$ by substituting k $=0,128,256,384$ in the DFT formula H$[$k$]=511$ n$=0$ h$[$n$]$e$$jk $2$ $512$ n c$)$ Now, show H$[0]=$ H$[128]=$ H$[256]=$ H$[384]=0$ directly using part a$.$ Recall that H$[$k$]$ is a sampled version of H$($ej$),$ i$.$e$.,$ the DTFT of h$[$n$].$ You also need to recall the relation between H$($z$)$ and H$($ej$)$