$[$Vaidyanathan $4\mathrm{.}13($extra credit $0\mathrm{.}5\%)]$ Let H$($z$)=($a $+$ z$1)/(1+$ az$1).$

$($a$)(10$ Pts$)$ Compute its polyphase components H$0($z$)$ and H$1($z$)$ so that H$($z$)=$ H$0($z$2)+$ z$1$H$1($z$2).$

$($b$)(10$ Pts$)$ Compute the magnitude response of H$($z$).$ Is H$($z$)$ an allpass system?

$($c$)(10$ Pts$)$ Compute the magnitude response of H$0($z$)$ and H$1($z$).$ Are H$0($z$)$ and H$1($z$)$ also allpass systems?