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GATE ECE 2010 | Question-42

The transfer function of a discrete time LTI system is given by
$$H(z)=\frac{2-\frac{3}{4} z^{-1}}{1-\frac{3}{4} z^{-1}+\frac{1}{8} z^{-2}}$$

Consider the following statements:
$\text{S1:}$ The system is stable and causal for $\text{ROC:} \; |z|>\frac{1}{2}$
$\text{S2:}$ The system is stable but not causal for $\text{ROC:} \; |z|<\frac{1}{4}$
$\text{S3:}$ The system is neilher stable nor causal for $\text{ROC:} \; \frac{1}{4}<|z|<\frac{1}{2}$

Which one of the following statements is valid?

  1. Both $\mathrm{Sl}$ and $\mathrm{S} 2$ are true
  2. Both $\mathrm{S} 2$ and $\mathrm{S} 3$ are true
  3. Both $\text{S1}$ and $\text{S3}$ are true
  4. $\text{S1, S2}$ and $\text{S3}$ are all true
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