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The system described by the difference equation y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1) has y(n) = 0 and n < 0. If x(n) = δ(n) then y(2) will be—
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- 2
- 1
- 0
- – 1
Correct Option: C
Given equation is
y(n) – 2y(n – 1) + y(n – 2) = x(n) – x(n – 1)
Taking z-transform on both side
Y(z) – 2Y(z).z–1 + Y(z).z–2 = X(z) – X(z).z–1
or
| = | = | |||
| X(z) | 1 – 2z–1 + z–2 | (1 – z – 1)2 |
or
| H(z) = | |
| 1 – z–1 |
or
h(n) = 1.u(n)
Now, y(n) = h(n).x(n)
y(n) = 1.u(n).δ(n)
y(2) = 0
Hence, alternative (C) is the correct choice.
