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The difference equation representat ion for a system is
y[n] – 2y [n – 1] + y[n – 2] = x[n] – x[n – 1]
If y[n] = 0 for n < 0 and x[n] = δ[n],
then y[2] will be
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- 2
- – 2
- – 1
- 0
Correct Option: D
For n = 0,
y[0] = x[0] – x[– 1]
For n = 1,
y[1] = 2y[0] + x[1] – x[0]
⇒ y[1] = x[0] + x[1] – 2x[– 1]
For n = 2,
y[2] = 2y[1] – y[0] + x[2] – x[1]
y[2] = x[0] + x[1] + x[2] – 3x[– 1]
y[2] = ?[0] + ?[1] + ?[2] – 3?[– 1] = 0
