Discussion
Z-transform of x (-n) is :
Answer: D
The Z-transform of \(x(-n)\) is \(X(Z^{-1})\).
By definition \(X(z) = \sum_{n} x(n) z^{-n}\). For the time-reversed sequence, substitute \(m = -n\):
\[ \begin{aligned} \sum_{n} x(-n) z^{-n} &= \sum_{m} x(m) (z^{-1})^{-m} \\ &= X(z^{-1}) \end{aligned} \]
Time reversal therefore replaces \(z\) by \(1/z\), and the region of convergence is inverted too. X(Z) is the transform of the original sequence, \(X(Z^{-2})\) would correspond to reversal combined with up-sampling by 2, and X(n) mixes the time and transform domains.
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