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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)1๐‘Ža1โ€‹ d)๐‘Ž๐‘›a n

Question

Which of the following is the inverse Z - transform of

\frac{z}{z-a} \quad (|z| > a) ?

a) aโˆ’na^{-n}

b) aa

c) 1a\frac{1}{a}

d) ana^n

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Solution

The inverse Z-transform of ๐‘ง/(๐‘งโˆ’๐‘Ž) where โˆฃ๐‘งโˆฃ>๐‘Ž is ๐‘Ž^n. So, the correct answer is d) ๐‘Ž^n.

Here's the step-by-step solution:

  1. The given function is ๐‘ง/(๐‘งโˆ’๐‘Ž).
  2. The standard formula for inverse Z-transform is ๐‘ง/(๐‘งโˆ’๐‘Ž) = ๐‘Ž^n.
  3. Therefore, the inverse Z-transform of the given function is ๐‘Ž^n.

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