Which of the following is the inverse Z - transform of ๐‘ง๐‘งโˆ’๐‘Ž(โˆฃ๐‘งโˆฃ>๐‘Ž)zโˆ’azโ€‹ (โˆฃzโˆฃ>a) ?a)๐‘Žโˆ’๐‘›a โˆ’n b)ac)๐‘Ž๐‘›a n d)1๐‘Ža1โ€‹

Question

Which of the following is the inverse Z - transform of ๐‘ง๐‘งโˆ’๐‘Ž(โˆฃ๐‘งโˆฃ>๐‘Ž)zโˆ’azโ€‹ (โˆฃzโˆฃ>a) ?a)๐‘Žโˆ’๐‘›a โˆ’n b)ac)๐‘Ž๐‘›a n d)1๐‘Ža1โ€‹
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Solution 1

The inverse Z-transform of ๐‘ง/(๐‘งโˆ’๐‘Ž) (for |๐‘ง|>๐‘Ž) is ๐‘Ž^n. So, the correct answer is c) ๐‘Ž^n.

Here's a step-by-step explanation:

  1. The Z-transform pairs are defined as ๐‘ง^n โ†” ๐‘Ž^n, where โ†” denotes a transform pair.

  2. The given function is ๐‘ง/(๐‘งโˆ’๐‘Ž), which can be rewritten as 1/(1-๐‘Ž/๐‘ง) by dividing the Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to so

dividing the Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem. Knowee AI StudyGPT is a powerful AI-powered study tool designed to he

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