x(n) and output y(n) of a system are related as $y (n) = 0.2 x (n) - 0.5 x (n - 2) + 0.4 x (n - 3)$ .
If the input applied is $[- 1, 1, 0 - 1]$ . Then the output at $n = 6$ is _____.
-0.4

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Solution

The correct option is A -0.4
$Y (z) = 0.2 X (z) - 0.5 z^{- 2} X (z) + 0.4 z^{- 3} X (z)$

$x (n) = [- 1, 1, 0, - 1]$

$= - 1 δ (n) + 1 δ (n - 1) + 0 δ (n - 2) - 1 δ (n - 3)$

$X (z) = - 1 + z^{- 1} - z^{- 3}$

$Y (z) = X (z) . H (z) = (0.2 - 0.5 z^{- 2} + 0.4 z^{- 3}) (- 1 + z^{- 1} - z^{- 3})$

$= - 0.2 + 0.2 z^{- 1} + 0.5 z^{- 2} - 1.1 z^{- 3} + 0.4 z^{- 4} + 0.5 z^{- 5} - 0.4 z^{- 6}$

$y (n) = [- 0.2, 0.2, 0.5, - 1.1, 0.4, 0.5, - 0.4]$

$y (n) = - 0.4$

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