The transfer function of a discrete time LTI system is given byH( z ) = 2 - 34z^ - 11 - 34z^ - 1 + 18z^ - 2 Consider the following statements: S1 : The system is stable and causal for ROC:| z | > 12 S2 : The system is stable but not causal for ROC:| z | < 14 S3 : The system is neither stable nor causal for ROC:14 < | z | < 12 Which one of the following statements is valid?

This question belongs to Electronics And Communications Engineering Signal Processing

Signal Processing

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 & Solution

Correct Answer: Option C

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