TIFR ECE 2013 | Question: 7

Question

The $Z$-transform of $\{x(n)\}$ is defined as $X(z)=\sum_{n} x(n) z^{-n}$ (for those $z$ for which the series converges). Let $u(n)=1$ for $n \geq 0$ and $u(n)=0$ for $n<0$. The inverse $Z$-transform of $X(z)=$ $\log (1-a z),|z|<1 / a$ is

• A. $a^{n} u(n-1) / n$
• B. $a^{-n} u(-n-1) / n$
• C. If $|a|<1$, then the answer is (a), otherwise the inverse is not well-defined
• D. If $|a|<1$, then the answer is (b), otherwise the inverse is not well-defined
• E. None of the above