Lecture 31 : Z Transform and Region of Convergence
Nature of Region of Convergence
Laplace Transform:
The ROC of the Laplace transform
X(s) of a two-sided signal lies between two vertical lines in the s-plane.
and
depend only on real part of s. For a right-sided signal
and the corresponding ROC is referred to as right-half plane. Similarly for a left-sided signal . This ROC is referred to as left-half plane. When x(t)
is two-sided i.e; of infinite extent for both t > 0 and t < 0 ; both
and
are finite and the ROC thus turns out to be a vertical strip in the s-plane.
Z-transform:
The ROC of X(z)
of a two sided signal consists of a ring in the z-plane centered about the origin.
and
depend only on magnitude of z. As in the case of Laplace transform
for a right-sided sequence and
for a left-sided sequence. If
x[n] is two-sided ;the ROC will consist of a ring with both
and
finite and non-zero.
and
depend only on real part of s. For a right-sided signal
and the corresponding ROC is referred to as right-half plane. Similarly for a left-sided signal 
. This ROC is referred to as left-half plane. When x(t)
is two-sided i.e; of infinite extent for both t > 0 and t < 0 ; both
for a left-sided sequence. If
x[n] is two-sided ;the ROC will consist of a ring with both
