Please answer Ztransform What is the requirement on the regi

Please answer:

(Z-transform) What is the requirement on the region of convergence of a system function H(z) for a discrete-time LTI system to be stable? What is the requirement on the region of convergence of a system function H(z) for a discrete-time LTI system to be causal? The system function of a discrete-time LTI system is given by H(z) = 1/(1-1/2 z^-1)(1+1/3 z^-1), |z| > 1/2 Sketch the pole zero plot of H(z) and shade the region of convergence. Is the system in part (c) stable? Why? Is the system in part (c) causal? Why?

Solution

a

Answer:

The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges.