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Which of the following represents the region of convergence (ROC) of a causal sequence in the Z-domain?
Question

Which of the following represents the region of convergence (ROC) of a causal sequence in the Z-domain?

A.

Inside the unit circle

B.

Entire Z-plane

C.

Outside the outermost pole

D.

Between two poles

Correct option is C

For a causal sequence (right-sided sequence) in the z-domain: The Region of Convergence (ROC) lies outside the magnitude of the outermost pole. It extends to infinity in the z-plane. This condition ensures that the z-transform converges for causal systems.Summary of ROC properties: Causal sequence: ROC is outside the outermost pole Anti-causal sequence: ROC is inside the innermost pole Two-sided sequence: ROC lies between poles\text{For a causal sequence (right-sided sequence) in the } z\text{-domain:} \\[8pt]\bullet \ \text{The Region of Convergence (ROC) lies outside the magnitude of the outermost pole.} \\[4pt]\bullet \ \text{It extends to infinity in the } z\text{-plane.} \\[4pt]\bullet \ \text{This condition ensures that the } z\text{-transform converges for causal systems.} \\[10pt]\textbf{Summary of ROC properties:} \\[6pt]\bullet \ \text{Causal sequence: ROC is outside the outermost pole} \\[4pt]\bullet \ \text{Anti-causal sequence: ROC is inside the innermost pole} \\[4pt]\bullet \ \text{Two-sided sequence: ROC lies between poles}​​

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