Properties of Laplace and Z-Transform(contd.)

3) Time Shift

For Laplace transform:

If  with ROC = R

then

   with ROC = R

For z-transform:

If  with ROC = R

then

Because of with ROC = R except for the possible addition or deletion of the origin or infinity

the multiplication by   for   poles will be introduced at z=0, which may cancel corresponding zeroes of X(z) at z=0. In this case the ROC for   equals the ROC of X(z) but with the origin deleted. Similarly, if   may get deleted.