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##### 6.8 z-TRANSFORM OF DELAYED UNIT SAMPLE SEQUENCE

The delayed unit sample sequence is expressed by

x1(n) = δ (nk) 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

Z [x(nk)] = zkX(z)

Applying this property to x1(n) = δ (nk), we have

Z[x1(n)] = Z[δ (nk)] = zkZ[δ (n)] = zk.1 = zk     (6.56)

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)] = Z[δ (n + k)] = zkZ[δ (n)] = zk.1 = zk

Z[x2(n)] has infinite value at z = ∞ ...

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