The transfer function of a discrete time LTI system is given by$$H\left( z \right) = \frac{{2 - \frac{3}{4}{z^{ - 1}}}}{{1 - \frac{3}{4}{z^{ - 1}} + \frac{1}{8}{z^{ - 2}}}}$$
Consider the following statements:
S1 : The system is stable and causal for $${\text{ROC}}:\left| z \right| > \frac{1}{2}$$
S2 : The system is stable but not causal for $${\text{ROC}}:\left| z \right| < \frac{1}{4}$$
S3 : The system is neither stable nor causal for $${\text{ROC}}:\frac{1}{4} < \left| z \right| < \frac{1}{2}$$
Which one of the following statements is valid?
A. Both S1 and S2 are true
B. Both S2 and S3 true
C. Both S1 and S3 are true
D. S1, S2 and S3 are all true
Answer: Option C
This Question Belongs to Electronics And Communications Engineering >> Signal Processing
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