TIFR ECE 2011 | Question: 6

Question

Let $\mathrm{H}(\mathrm{z})$ be the $z$-transform of the transfer function corresponding to an input output relation $y(n)-\frac{1}{2} y(n-1)=x(n)+\frac{1}{3} x(n-1)$. Then which of the following is TRUE

• A. The $\operatorname{ROC}$ of $\mathrm{H}(\mathrm{z})$ is $|z|>\frac{1}{2}$.
• B. The $\operatorname{ROC}$ of $\mathrm{H}(\mathrm{z})$ is $|z|<\frac{1}{2}$.
• C. $\operatorname{Both}$ (a) and (b).
• D. System is necessarily causal.
• E. None of the above.