Question

Consider a sequence

x1[n]x_1[n]

with z-transform

X1(z)X_1(z)

and a sequence

x2[n]x_2[n]

with z-transform

X2(z)X_2(z)

, where

x2[n]=x1[n]x_2[n]=x_1[-n]

. Show that

X2(z)=X1(1/z)X_2(z)=X_1(1/z)

, and from his, show that if

X1(z)X_1(z)

has a pole (or zero ) at

z=z0z=z_0

, then

X2(z)X_2(z)

has a pole (or zero) at

z=1/z0.z=1/z_0.

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