$A shifted ramp sequence is given as x [n] = r [n + 2] - r [n + 1] - 3 r [n - 1] + 3 r [n - 2] The final value of the sequence x[n] is______$
-2

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Solution

The correct option is A -2
$Given ramp sequence,$

$x [n] = r [n + 1] - r [n + 1] - 3 r [n - 1] + 3 r [n - 2]$

$= (n + 2) u [n + 2] - n (n + 1) u [n + 1] - 3 (n - 1) u [n - 1] + 3 (n - 2) u [n - 2]$

$∴ Sum of co-efficients of shifed step sequences will result in the final value$

$∴ x [\infty] = (n + 1) - (n - 1) - 3 (n - 1) + 3 (n - 2)$

$x [\infty] = - 2$

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