Question

What is the set of all values of z for which X(z) attains a finite value?

(a) Radius of convergence

(b) Radius of divergence

(c) Feasible solution

(d) None of the mentioned

This question was posed to me by my college professor while I was bunking the class.

This interesting question is from Z Transform topic in section Z Transform and its Application – Analysis of the LTI Systems of Digital Signal Processing

Answer 1

Right option is (a) Radius of convergence

Explanation: Since X(z) is a infinite power series, it is defined only at few values of z. The set of all values of z where X(z) converges to a finite value is called as Radius of Convergence(ROC).