Finding x[0] from the region of convergence

1. How do you find the region of convergence?
2. How do you find the region of convergence in Z transform?
3. What are the properties of region of convergence?
4. What is the Z transform of the signal XNO =[ 3 2n )- 4 3n )] Uno?

How do you find the region of convergence?

Perhaps the best way to look at the region of convergence is to view it in the s-plane. What we observe is that for a single pole, the region of convergence lies to the right of it for causal signals and to the left for anti-causal signals.

How do you find the region of convergence in Z transform?

For x(n)=δ(n), i.e., impulse sequence is the only sequence whose ROC of Z-transform is the entire z-plane. If x(n) is an infinite duration causal sequence, then its ROC is |z|>a, i.e., it is the exterior of a circle of the radius equal to a.

What are the properties of region of convergence?

Properties of ROC of Laplace Transform

ROC contains strip lines parallel to jω axis in s-plane. If x(t) is absolutely integral and it is of finite duration, then ROC is entire s-plane. If x(t) is a right sided sequence then ROC : Res > σ_o. If x(t) is a left sided sequence then ROC : Res < σ_o.

What is the Z transform of the signal XNO =[ 3 2n )- 4 3n )] Uno?

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