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The causal sequence f(n) if f(z) = 1 1 - 1 z-1 2 2
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1 n + n 1 n u[n] 2 2 -
1 n + n 1 n u[n] 2 2 2 -
1 n – n 1 n u[n] 3 3 -
1 n + n 1 n u[n] 3 3
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Correct Option: B
We will apply same approach as discussed in above problem.
(A) | ![]() | ![]() | ![]() | n | + n | ![]() | ![]() | n | ![]() | u(n) | ||
2 | 2 |
∴ | ![]() | ![]() | n | ←z→ | ||||||
2 | 1 - | z-1 | ||||||||
and n | ![]() | ![]() | n | ←z→ | |||||||
2 | ![]() | 1 - | z-1 | ![]() | 2 | ||||||
Now, | ![]() | ![]() | ![]() | n | + n | ![]() | ![]() | n | ![]() | u(n) | ||
2 | 2 |
= | + | |||||||||
1 - | z-1 | ![]() | 1 - | z-1 | ![]() | 2 | ||||
= | 1 – | z– 1 | + z– 1 | ||
2 | |||||
![]() | 1 – | z– 1 | ![]() | 2 | |
2 |
= | 1 + | z– 1 | |||
2 | |||||
![]() | 1 – | z– 1 | ![]() | 2 | |
2 |
Since, (A) is not the correct choice, so we will solve for next option, i.e., (B).
![]() | ![]() | ![]() | n | + | ![]() | ![]() | n | ![]() | u[n] | ||||
2 | 2 | 2 |
↔ | + | |||||||||||
1 - | z-1 | 2 | ![]() | 1 - | z-1 | ![]() | 2 | |||||
↔ | ![]() | 1 – | z– 1 | ![]() | + z– 1 | |
2 | ||||||
![]() | 1 – | z– 1 | ![]() | 2 | ||
2 |
↔ | ||||||
2 | ![]() | 1 - | z-1 | ![]() | 2 | |
↔ | ||||||
2 | ![]() | 1 - | z-1 | ![]() | 2 | |
↔ | ||||||
![]() | 1 - | z-1 | ![]() | 2 | ||
Therefore, option (B) is the correct choice.