RoC of Z transform of signal consisting of 3 values

1. What is the ROC of the z-transform of the signal?
2. How many Poles can Roc of z-transform contain?
3. What is the z-transform of the signal x n )= 3 2 n )- 4 3 n u n?
4. What is the ROC of z-transform of an two sides infinite sequence?

What is the ROC of the z-transform of the signal?

The ROC of the Z-transform is a ring or disc in the z-plane centred at the origin. The ROC of the Z-transform cannot contain any poles. The ROC of Z-transform of an LTI stable system contains the unit circle.

How many Poles can Roc of z-transform contain?

The ROC cannot contain any poles.

By definition a pole is a where X(z) is infinite. Since X(z) must be finite for all z for convergence, there cannot be a pole in the ROC. If x[n] is a finite-duration sequence, then the ROC is the entire z-plane, except possibly z=0 or |z|=∞.

What is the z-transform of the signal x n )= 3 2 n )- 4 3 n u n?

What is the z-transform of the signal x(n)=[3(2ⁿ)-4(3ⁿ)]u(n)? => X(z)=\frac31-2z^-1-\frac41-3z^-1.

What is the ROC of z-transform of an two sides infinite sequence?

What is the ROC of z-transform of an two sided infinite sequence? Explanation: Let us plot the graph of z-transform of any two sided sequence which looks as follows. From the above graph, we can state that the ROC of a two sided sequence will be of the form r2 < |z| < r1.