$3-$ Consider a system with two complex conjugate poles at p$1,2=$ re$$j$$:

H$($z$)$

$=$

bo

bo

$(1$ rej$$z$1)(1$ re $$j$$z$1)1-(2$r cos p$)$z$-1+$ r$2$z$2\text{'}$

a$-$ Find the input$-$output relationship

b$-$ Find the impulse response

c$-$Find geometrical pole$-$zero pattern, and magnitude response,

d$-$ Change the H$($z$)$ transfer function to compensate for a high quality BPF