#### Question

Consider a sequence

$x_1[n]$

with z-transform

$X_1(z)$

and a sequence

$x_2[n]$

with z-transform

$X_2(z)$

, where

$x_2[n]=x_1[-n]$

. Show that

$X_2(z)=X_1(1/z)$

, and from his, show that if

$X_1(z)$

has a pole (or zero ) at

$z=z_0$

, then

$X_2(z)$

has a pole (or zero) at

$z=1/z_0.$

#### Solution

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