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The amplitude response of a discrete system with a simple pole is shown in the given figure.
The must be located—
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- On the real axis at z = 1
- On the real axis at z = – 1
- At the origin of the z-plane
- At z = ∞
Correct Option: B
From given figure Function say x(n) represented as 
x(n) = (– 1)n u(n) Now, X(z)
| X(z) = |  | x(n)·z–n |
or
| X(z) = | | (– 1)n·z–n |
or
X(z) = 1 + (– 1)z–1 + z–2 + (– 1)–3 + …
or
| X(z) = | |
| 1 + z–1 |
or
| X(z) = | |
| z + 1 |
Here, pole at z + 1 = 0
i.e., z = – 1
Hence, alternative (B) is the correct choice.
