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If Z transform of x(n) is X(z) then the Z transform of x(n - k) is _______
1. X(z-k z)
2. X(zk z)
3. z-k X(z)
4. zk X(z)

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Correct Answer - Option 3 : z-k X(z)

Definition:

Z transform is defined as

\(X\left( z \right) = \mathop \sum \limits_{ - \infty }^\infty x\left[ n \right]{z^{ - n}}\)

Time-shifting:

If X(z) is a z transform of x(n), then the z transform of x(n – n0) is,

\(x\left( {n - {n_0}} \right) \leftrightarrow {z^{ - {n_0}}}X\left( z \right)\)

Analysis:

\(x\left( {n - {k}} \right) \leftrightarrow {z^{ - {k}}}X\left( z \right)\)

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