The delayed unit sample sequence is expressed by

*x*_{1}(*n*) = *δ* (*n* − *k*) for right shift and also by *x*_{2}(*n*) = *δ* (*n* + *k*) for left shift.

We have already shown that *Z*[*δ* (*n*)] = 1 where ROC is entire *z*-plane.

Using shifting property of *z*-transform we can write

Applying this property to *x*_{1}(*n*) = *δ* (*n* − *k*), we have

*Z*[*x*_{1}(*n*)] has infinite value at *z* = 0 whereas it has finite values for all remaining values of *z*

Therefore, the ROC of *Z*[*x*_{1}(*n*)] is entire *z*-plane except at *z* = 0.

Applying this property to *x*_{2}(*n*) = *δ*(*n* + *k*), we have

*Z*[*x*_{2}(*n*)] has infinite value at *z* = ∞ ...

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