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From Z-transfer function to real sequence

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neoflash

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causal right hand sequence

Can I say that a Z-transfer function will represent a unique sequence, only when the initial condition is causal?
 

No this is not correct. Z-transfer function will represent a unique sequence, only when the converge zone is defined
 

It depends on the converge zone. A left-hand sequence and a right-hand sequence may have the same Z-transfer function,but their converge zone is different.
 

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