Final value of the signal, for which the corresponding z-transform is
$X (z) = \frac{2 z^{- 1}}{1 - 1.8 z^{- 1} + 0.8 z^{- 2}}$
10

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Solution

The correct option is A 10
Using final value theorem,

$x (\infty) = lim z \to 1 (1 - z^{- 1}) X (z)$

$x (\infty) = lim z \to 1 \frac{(1 - z^{- 1}) 2 z^{- 1}}{(1 - z^{- 1}) (1 - 0.8 z^{- 1})} = \frac{2}{0.2} = 10$

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Consider the z-transform X (z) = \frac{10 - 8 z^{- 1}}{2 - 5 z^{- 1} + 2 z^{- 2}} if ROC includes unit circle then the value of x(1) is

X (z) = \frac{z}{1 - z^{- 5}}

x [0] + x [- 1] + x [2] + x [3] + x [4]

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