onsider the filter, relating the infinite duration discrete$-$time sequences x$[$n$]$ and y$[$n$]$:

y$[$n$]=$a$1$y$[$n$1]+$ b$0$x$[$n$]+$ b$1$x$[$n$1]$ n$=$$,...,$ $(4)$

Here, the filter coefficients a$1,$ b$0$ and b$1$ are real numbers.

a$)$ Find the transfer function H$($$)=$ Y$($$)/$X$($$),$ where Y$($$)$ and X$($$)$ are the DTFT of x$[$n$]$

and y$[$n$],$ respectively. E$.$g$.,$

X$($$)=$

n$=$

x$[$n$]$e$$jnT $(5)$

for sampling period T

b$)$ Find conditions on the coefficients a$1,$b$0$ and b$1$ such that the filter is all$-$pass, or that $|$H$($$)|=$

$1,$ for all with$$$/$T $$ $$$/$T$.($Be sure to point out which cases are trivial, or for which

H$($$)=1$ for all $.)$