Suppose x[n] is an absolutely summable discrete-time signal. Its
![Suppose x[n] is an absolutely summable discrete-time signal. Its](http://storage.googleapis.com/tb-img/production/19/11/F1_S.B_Madhu_18.11.19_D%207.png)
| Suppose x[n] is an absolutely summable discrete-time signal. Its z-transform is a rational function with two poles and two zeroes. The poles are at z = ±2j. Which one of the following statements is TRUE for the signal x[n]?
A. It is a finite duration signal.
B. It is a causal signal.
C. It is a non-causal signal.
D. It is a periodic signal.
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
- If a sequence is absolutely summable, then its DTFT will exist and the ROC will include the unit circle.
- If ROC includes the unit circle then the system will be a non-causal system, because causal systems are right-sided signals with ROC extending to the right side of z-plane.
Analysis:
- Given sequence is summable, so its ROC will include the unit circle, which implies that the DTFT exists.
- Poles location shown below:
- Here ROC includes the unit circle as can be easily seen from the above graph which means that the ROC is left sided.
- Hence it is a non-causal system
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So Option 3 is Correct.