The delayed unit sample sequence is expressed by
x1(n) = δ (n − k) for right shift and also by x2(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 x1(n) = δ (n − k), we have
Z[x1(n)] has infinite value at z = 0 whereas it has finite values for all remaining values of z
Therefore, the ROC of Z[x1(n)] is entire z-plane except at z = 0.
Applying this property to x2(n) = δ(n + k), we have
Z[x2(n)] has infinite value at z = ∞ ...