a$)(6$ points$)$ Find the transfer function H$($z$)$ of the above filter. What filter is this, lowpass, highpass,

bandpass, bandstop or allpass?

$($b$)(8$ points$)$ Now suppose d$1=1=3.$ Let x$[$n$]$ be a causal signal with finite energy:

$1$X

n$=0$

jx$[$n$]$j$2=10$

Can the output signal y$[$n$]$ have finite energy? If yes, compute the energy of y$[$n$].$ If not, explain why