GATE EC 2015 Set 3 — Question 52
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Signals & Systems → Discrete-Time Signals → Causality & Stability
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Question
Suppose is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at . Which one of the following statements is TRUE for the signal ?
Correct answer
(C) It is a non-causal signal.
Solution
For a signal to be absolutely summable, the Region of Convergence (ROC) of its z-transform must include the unit circle (). The given poles are at , which have a magnitude of .
1.If the signal were causal, the ROC would be , which does not include the unit circle.
2.If the signal were anti-causal, the ROC would be , which includes the unit circle.
3.If the signal were two-sided (non-causal), the ROC would be a ring between poles, but since there are only poles at , the ROC must be to include the unit circle.
In either the anti-causal or two-sided case, the signal is non-causal. A finite duration signal cannot have poles at (except at or ). A periodic signal is not absolutely summable. Thus, the signal must be non-causal.Continue learning with Success Tracker
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