Figure P

$1$

$.$

$8$

$9$

$$shows the block diagram of a first

$-$

order recursive discrete

$-$

time filter. This filter differs from that of Fig.

$1$

$.$

$6$

$9$

$$in that the output y

$[$

n

$]$

$$also requires knowledge of the past input x

$[$

n

$-$

$1$

$]$

$$for its evaluation. Building on the solution given in Eq

$.$

$($

$1$

$.$

$1$

$1$

$6$

$)$

$,$

$$derive an expression for the output y

$[$

n

$]$

$$in terms of the input x

$[$

n

$]$

$.$