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Causal sequence f(n) if f(z) = 4·z– 3 (1 – z– 1)2
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- 4(n – 2) u(n – 2)
- 4(n – 1) u(n – 1)
- 4(n – 3) u(n – 3)
- None of these
Correct Option: A
In order to solve such type of very confusing objective problems, start with option (A) and carried to the final option until the required value given in question meet.
(A) 4(n – 2) u(n – 2)
We know that
| x(n) = u(n) ←z→ | = X(z) | |
| z - 1 |
| nu(n) ↔ – z | X(z) | |
| dz |
| = – z |  |  | ||
| dz | z - 1 |
| = – z | |
| (z – 1)2 |
| (z – 1)2 |
| (z – 1)2 |
| (1 - z– 1)2 |
| 4(n – 2) u(n – 2) ↔ 4z–2 |  |  | |
| (1 - z– 1)2 |
| ↔ | |
| (1 – z–1)2 |
As we got the required solution in first attempt, so no need to solve for further options given in the problem.
Hence, obviously alternative (A) is the correct choice.
