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 If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)? 
  • a)
    |a|r1<|z|<|a|r2
  • b)
    |a|r1>|z|>|a|r2
  • c)
    |a|r1<|z|>|a|r2
  • d)
    |a|r1>|z|<|a|r2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)...
Explanation: Given ROC of X(z) is r1<|z|<r2
Then ROC of X(a-1z) will be given by r1<|a-1z |<r2=|a|r1<|z|<|a|r2
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Most Upvoted Answer
If the ROC of X(z) is r1<|z|<r2, then what is the ROC of X(a-1z)...
If the ROC (Region of Convergence) of X(z) is r1, it means that the Z-transform X(z) converges for all values of z within the region r1. In other words, r1 represents the set of values for which the Z-transform of a discrete-time signal X(n) converges.

The ROC can have different shapes, depending on the properties of the signal X(n). It can be a circular region, an annular region, or extend to infinity. The choice of r1 determines the convergence properties of the Z-transform and is important for analyzing and manipulating the signal in the Z-domain.

It is worth noting that the ROC is typically specified as a range of values, such as |z| > r1 or r1 < |z|="" />< r2,="" where="" r1="" and="" r2="" represent="" the="" radius="" of="" convergence.="" r2,="" where="" r1="" and="" r2="" represent="" the="" radius="" of="" />
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