GATE EC 2014 Set 1 — Question 53
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Signals & Systems → Discrete-Time Signals → Region of Convergence
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Question
Let . The Region of Convergence (ROC) of the z-transform of is
Correct answer
(C) (1)/(3) z (1)/(9)
Solution
The z-transform of is given by .
For , the z-transform is with ROC .
For , the z-transform is with ROC .
The overall ROC is the intersection of the individual ROCs: .
For , the z-transform is with ROC .
For , the z-transform is with ROC .
The overall ROC is the intersection of the individual ROCs: .
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