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Z transform and associated ROC for the sequence x[n] = a– n u[– n] is—
-
-
(1 + az), |z| > 1 |a| -
1 , |z| < 1 1 + az |a| -
(1 – az), |z| > 1 |a| -
1 , |z| < 1 (1 – az) |a|
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Correct Option: D
As we know that
| x[n] = an u[n] ←z→ | = x(z), |z| > |a| | |
| z - a |
By using time reversal property
| x[- n] ←z→ | = x(z), |z| < |a| | |
| z - a |
| So, a–n u[– n]←z→ | =|z| < | ||
| z- 1 - a | |a| |
or
| or, a–n u[– n]←→ | |
| 1 - az |
Hence, alternative (D) is the correct choice.
