The transfer function of a discrete time LTI system is given by H( z ) = 2 - 3 over 4z^ - 1 over 1 - 3 over 4z^ - 1 + 1 over 8z^ - 2 Consider the following statements: S1 : The system is stable and causal for ROC:| z | > 1 over 2 S2 : The system is stable but not causal for ROC:| z | < 1 over 4 S3 : The system is neither stable nor causal for ROC:1 over 4 < | z | < 1 over 2 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
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S₂ : The system is stable but not causal for
$$ROC:\left| z \right| < {1 \over 4}$$
S₃ : The system is neither stable nor causal for
$$ROC:{1 \over 4} < \left| z \right| < {1 \over 2}$$
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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