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GATE EE 2020 Set 1 — Question 14

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MCQ+1 / -0.33EasyZ Transform & ROCLaplace & Z TransformsSignals & Systems

Signals & Systems → Laplace & Z Transforms → Z Transform & ROC

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Consider a signal x[n]=(12)n1[n]x[n] = \left(\frac{1}{2}\right)^n 1[n], where 1[n]=01[n] = 0 if n<0n < 0, and 1[n]=11[n] = 1 if n≥0n \geq 0. The zz-transform of x[n−k]x[n - k], k>0k > 0 is z−k1−12z−1\frac{z^{-k}}{1 - \frac{1}{2}z^{-1}} with region of convergence being
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