X (z) = ln (1 + z-1 ), |z|>0
If z-transform is given by
X (z) = cos ( z -3), |z|> 0,
The value of x is
X (z) of a system is specified by a pole zero pattern in fig. P.5.4.36.
Consider three different solution of x[n]
Correct solution is
All gives the same z transform with different ROC. So all are the solution.
Consider three different signal
Fig. P.5.4.37 shows the three different region. Choose the correct option for the ROC of signal
x1[n] is right-sided signal
For three different ROC consider there different solution of signal x[n] :
Correct solutions are
So (b) is wrong.
X (z) has poles at z = 1/2 and z = -1. If x  = 1 x [ -1] = 1, and the ROC includes the point z = 3/4. The time signal x[n] is
Since the ROC includes the Z = 3/4, ROC is
x[n] is right-sided, X (z) has a signal pole, and x = 2, x = 1/2. x[n] is
The z-transform function of a stable system is given as
The impuse response h[n] is
h[n] is stable, so ROC includes |z|= 1
Let The unilateral z-transform is